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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)

Cbse's question bank on case study for class 10 maths chapter 7 is available here. practice this new type of questions to score good marks in your board exam..

Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry

CASE STUDY 1:

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.

1. Find the position of green flag

b) (2,0.25)

d) (0, -25)

Answer:  a) (2,25)

2. Find the position of red flag

Answer: c) (8,20)

3. What is the distance between both the flags?

a) √41

b) √11

c) √61

d) √51

Answer: c) √61

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

d) (2.5,20)

Answer: a) (5, 22.5)

5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

Answer: a) (3.5,24)

CASE STUDY 2:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

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Case Study Class 10 Maths Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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• Class 12 Maths Case Study Questions
• CBSE Reduced Syllabus Class 10 (2020-21)
• Class 10 Maths Basic Sample Paper 2024
• How to Revise CBSE Class 10 Maths in 3 Days
• CBSE Practice Papers 2023
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• Competency Based Learning in CBSE Schools

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CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) The expression of the polynomial represented by the graph is

(iii) Find the value of the polynomial represented by the graph when x = 6.

(iv) The sum of zeroes of the polynomial x 2  + 2x - 3 is

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

(ii) Find the value of \(\alpha\) + \(\beta\) +  \(\alpha\) \(\beta\) .

(iii) The value of p(2) is

(iv) If \(\alpha\) and \(\beta\) are zeroes of  \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)

(v) If sum of zeroes of  \(q(x)=k x^{2}+2 x+3 k\)  is equal to their product, then k =

(ii) The axis of symmetry of the given parabola is

(iii) The zeroes of the polynomial, represented in the given graph, are

(iv) Which of the following polynomial has -2 and -3 as its zeroes?

(v) For what value of 'x', the value of the polynomial  \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)

(ii) What will be the expression of the polynomial given in diagram?

(iii) What is the value of the polynomial, represented by the graph, when x = 4?

(iv) If the tunnel is represented by x 2  + 3x - 2, then its zeroes are

(v) If one zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is

(ii) The sum of product of zeroes taken two at a time is

(iii) Product of zeroes of polynomial p(x) is

(iv) The value of the polynomial p(x), when x = 4 is

(v) If  \(\alpha,\beta,\gamma\)  are the zeroes of a polynomial g(x) such that  \(\alpha+\beta+\gamma=3, \alpha \beta+\beta \gamma+\gamma \alpha=-16\)   and  \(\alpha \beta \gamma=-48\)   then, g(x) =

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Cbse 10th standard maths subject polynomials case study questions with solution 2021 answer keys.

(i) (b): Graph of a quadratic polynomial is a parabolic in shape. (ii) (c): Since the graph of the polynomial cuts the x-axis at (-6,0) and (6, 0). So, the zeroes of polynomial are -6 and 6. \(\therefore\) Required polynomial is p(x) = x 2 - (-6 + 6)x + (-6)(6) = x 2 - 36 (iii) (c) : We have, p(x) = x 2 - 36 Now, p( 6) = 62 - 36 = 36 - 36 = 0 (iv) (b): Letf (x) = x 2 + 2x - 3. Then, \(\text { Sum of zeroes }=-\frac{\text { coefficient of } x}{\text { coefficient of } x^{2}}=-\frac{(2)}{1}=-2\) (v) (d): The given polynomial is at 2 + 5t + 3a Given, sum of zeroes = product of zeroes. \(\Rightarrow \quad \frac{-5}{a}=\frac{3 a}{a} \Rightarrow a=\frac{-5}{3}\)

(i) (b): Given, a and \(\beta\) are the zeroes of  \(p(x)=x^{2}-24 x+128\) \(\text { Putting } p(x)=0 \text { , we get }\) \( x^{2}-8 x-16 x+128=0 \) \(\Rightarrow x(x-8)-16(x-8)=0 \) \(\Rightarrow (x-8)(x-16)=0 \Rightarrow x=8 \text { or } x=16 \) \(\therefore \alpha=8, \beta=16\) (ii) (c) :  \(\alpha+\beta+\alpha \beta =8+16+(8)(16) =24+128=152 \) (iii) (d) :  \(p(2)=2^{2}-2 4(2)+128=4-48+128=84\) (iv) (a): Since a and \(\beta\) are zeroes of  \(x^{2}+x-2\) \(\therefore \quad \alpha+\beta=-1 \text { and } \alpha \beta=-2 \) \(\text { Now, } \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha \beta}=\frac{-1}{-2}=\frac{1}{2}\) (v) (c): Sum of zeroes  \(=\frac{-2}{k}\) Product of zeroes  \(=\frac{3 k}{k}=3\) According to question, we have  \(\frac{-2}{k}=3\) \(\Rightarrow \quad k=\frac{-2}{3}\)

(i) (b): The shape of the path of the soccer ball is a parabola. (ii) (c): The axis of symmetry of the given curve is a line parallel to y-axis. (iii) (a): The zeroes of the polynomial, represented in the given graph, are -2 and 7, since the curve cuts the x-axis at these points. (iv) (d): A polynomial having zeroes -2 and -3 is  \(p(x)=x^{2}-(-2-3) x+(-2)(-3)=x^{2}+5 x+6\) (v) (c): We have  \(f(x)=(x-3)^{2}+9\) \(\text { Now, } 9=(x-3)^{2}+9 \) \(\Rightarrow(x-3)^{2}=0 \Rightarrow x-3=0 \Rightarrow x=3\)

(i) (a): Since, the graph intersects the x-axis at two points, namely x = 8, -2. So, 8, - 2 are the zeroes of the given polynomial. (ii) (b): The expression of the polynomial given in diagram is  \(-x^{2}+6 x+16\) (iii) (c) : Let  \(p(x)=-x^{2}+6 x+16\) \(\text { When } x=4, p(4)=-4^{2}+6 \times 4+16=24\) (iv) (d): Let  \(f(x)=-x^{2}+3 x-2\) Now, consider  \(f(x)=0 \Rightarrow-x^{2}+3 x-2=0\) \(\begin{aligned} &\Rightarrow x^{2}-3 x+2=0 \Rightarrow(x-2)(x-1)=0\\ &\Rightarrow x=1,2 \text { are its zeroes. } \end{aligned}\) (v) (b): Let a and \(\beta\)  are the zeroes of the required polynomial. Given  \(\alpha + \beta = - 3\) If \(\alpha\) = 4, then  \(\beta\) = -7 \(\therefore \quad \text { Representation of tunnel is }-x^{2}-3 x+28 \text { . }\)

(i) (c): For finding  \(\alpha,\beta,\)   \(\gamma\)  consider p(x) = 0 \(\Rightarrow \quad x^{3}-18 x^{2}+95 x-150=0 \) \(\Rightarrow \quad(x-3)\left(x^{2}-15 x+50\right)=0 \) \(\Rightarrow \quad(x-3)(x-5)(x-10)=0 \Rightarrow x=10 \text { or } x=5 \text { or } x=3 \) \(\text { Thus } \alpha=10, \beta=5 \text { and } \gamma=3\) (ii) (d): Here  \(\alpha=10, \beta=5 \text { and } \gamma=3\) \(\therefore\)   Sum of product of zeroes taken two at a time \(\begin{array}{l} =\alpha \beta+\beta \gamma+\gamma \alpha=(10)(5)+(5)(3)+(3)(10) \\ =50+15+30=95 \end{array}\) (iii) (a): Product of zeroes of polynomial p(x) =  \(\alpha\beta\gamma\) = (10) (5) (3) = 150 (iv) (b): We have  \(p(x)=x^{3}-18 x^{2}+95 x-150\) \(\begin{array}{l} \text { Now, } p(4)=4^{3}-18(4)^{2}+95(4)-150 \\ =64-288+380-150=6 \end{array}\) (v) (d):   \(g(x)=x^{3}-(\alpha+\beta+\gamma) x^{2} +(\alpha \beta+\beta \gamma+\gamma \alpha) x-\alpha \beta \gamma \) \(\Rightarrow g(x)=x^{3}-3 x^{2}-16 x-(-48)=x^{3}-3 x^{2}-16 x+48\)

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Case Study Questions for Class 10 Science Chapter 7 Control and Coordination

• Last modified on: 1 year ago
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Question 1:

Read the case/passage and answer the questions given below.

To carry out a simple function such as eating food there has to be coordination of the eyes, hands and the mouth. The eyes have to focus on the food, the hands have to pick it up and take it to the mouth where it will be chewed. All these actions have to be coordinated in such a manner that they follow a particular sequence and the action is completed. A similar mechanism is also needed for internal functions of the body. This function is carried out by the nervous system. It is composed of (a) Specialised cells which can detect, receive and transmit different kinds of stimuli. These are called neurons. (b) Nerve fibres which are certain bundles of extended processes of nerve cells.

The individuals also have to adjust to the changing conditions around them and vary their responses. At the same time, the internal conditions of the body should be maintained constant. This is called homeostasis. The internal conditions of the body are maintained at a constant by controlling the physiology of the organisms.

(i) What will the correct sequence in which conduction of information through nerves take place? (ii) How homeostasis is said to maintain the equilibrium of the body? (iii) What function does the central nervous system perform? (iv) What happens when the dendrite tip of a nerve cell receives a signal?

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CBSE Class 10 Maths: Case Study Questions of Chapter 7 Coordinate Geometry PDF Download

Case study Questions in the Class 10 Mathematics Chapter 7  are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 7  Coordinate Geometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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NCERT Solutions For Class 10 Maths Chapter 7 - Coordinate Geometry

Ncert solutions for class 10 maths chapter 7 – cbse free pdf download.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry covers all the exercises provided in the NCERT textbook. These NCERT solutions, prepared by experts at BYJU’S, are comprehensive study material for the students preparing for the CBSE Class 10 board examination. These solutions are available for easy access and download by the students. Here, you can get detailed stepwise answers to different types of questions provided in the NCERT textbook. Practising the Solutions of NCERT will help you attain perfection on the topics involved in the coordinate geometry chapter.

Download Exclusively Curated Chapter Notes for Class 10 Maths Chapter – 7 Coordinate Geometry

Download most important questions for class 10 maths chapter – 7 coordinate geometry.

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progressions
• Chapter 6 Triangles
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

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Access Answers to NCERT Solutions for Class 10 Maths Chapter 7

Exercise 7.1 page no: 161.

1. Find the distance between the following pairs of points:

(i) (2, 3), (4, 1)

(ii) (-5, 7), (-1, 3)

(iii) (a, b), (- a, – b)

Distance formula to find the distance between two points (x 1 , y 1 ) and (x 2 , y 2 ) is, say d,

2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns, A and B, discussed in Section 7.2?

Let us consider town A at point (0, 0). Therefore, town B will be at point (36, 15).

Distance between points (0, 0) and (36, 15)

In section 7.2, A is (4, 0) and B is (6, 0) AB 2 = (6 – 4) 2 – (0 – 0) 2 = 4

The distance between towns A and B will be 39 km. The distance between the two towns, A and B, discussed in Section 7.2, is 4 km.

3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Solution:   If the sum of the lengths of any two line segments is equal to the length of the third line segment, then all three points are collinear.

Consider, A = (1, 5) B = (2, 3) and C = (-2, -11)

Find the distance between points: say AB, BC and CA

Since AB + BC ≠ CA

Therefore, the points (1, 5), (2, 3), and (- 2, – 11) are not collinear.

4. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Since two sides of any isosceles triangle are equal, to check whether given points are vertices of an isosceles triangle, we will find the distance between all the points.

Let the points (5, – 2), (6, 4), and (7, – 2) represent the vertices A, B and C, respectively.

This implies whether given points are vertices of an isosceles triangle.

5. In a classroom, 4 friends are seated at points A, B, C and D, as shown in Fig. 7.8. Champa and Chameli walk into the class, and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.

From the figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).

Find the distance between points using the distance formula, we get

All sides are of equal length. Therefore, ABCD is a square, and hence, Champa was correct.

6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)

(ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4)

(iii) (4, 5), (7, 6), (4, 3), (1, 2)

(i) Let the points (- 1, – 2), (1, 0), ( – 1, 2), and ( – 3, 0) represent the vertices A, B, C, and D of the given quadrilateral, respectively.

Side length = AB = BC = CD = DA = 2√2

Diagonal Measure = AC = BD = 4

Therefore, the given points are the vertices of a square.

(ii) Let the points (- 3, 5), (3, 1), (0, 3), and (- 1, – 4) represent the vertices A, B, C, and D of the given quadrilateral, respectively.

It’s also seen that points A, B and C are collinear. So, the given points can only form 3 sides, i.e. a triangle and not a quadrilateral which has 4 sides. Therefore, the given points cannot form a general quadrilateral.

(iii) Let the points (4, 5), (7, 6), (4, 3), and (1, 2) represent the vertices A, B, C, and D of the given quadrilateral, respectively.

Opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.

7. Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).

To find a point on the x-axis.

Therefore, its y-coordinate will be 0. Let the point on the x-axis be (x,0).

Consider A = (x, 0); B = (2, – 5) and C = (- 2, 9).

Simplify the above equation,

Remove the square root by taking square on both sides, we get

(2 – x) 2 + 25 = [-(2 + x)] 2  + 81

(2 – x) 2 + 25 = (2 + x) 2  + 81

x 2  + 4 – 4x + 25 = x 2  + 4 + 4x + 81

8x = 25 – 81 = -56

Therefore, the point is (- 7, 0).

8. Find the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

Given: Distance between (2, – 3) and (10, y) is 10.

Using the distance formula,

Simplify the above equation and find the value of y.

Squaring both sides,

64 + (y + 3) 2 = 100

(y + 3) 2 = 36

y + 3 = +6 or y + 3 = −6

y = 6 – 3 = 3 or y = – 6 – 3 = -9

Therefore, y = 3 or -9.

9. If Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), find the values of x. Also, find the distance QR and PR.

Given: Q (0, 1) is equidistant from P (5, – 3) and R (x, 6), which means PQ = QR

Step 1: Find the distance between PQ and QR using the distance formula,

Squaring both sides to omit square root

41 = x 2  + 25

x = 4 or x = -4

Coordinates of Point R will be R (4, 6) or R (-4, 6),

If R (4, 6), then QR

10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Point (x, y) is equidistant from (3, 6) and (- 3, 4).

Squaring both sides, (x – 3) 2 +(y – 6) 2 = (x + 3) 2 +(y – 4) 2

x 2 + 9 – 6x + y 2 + 36 – 12y = x 2 + 9 + 6x + y 2 +16 – 8y

36 – 16 = 6x + 6x + 12y – 8y

20 = 12x + 4y

3x + y – 5 = 0

Exercise 7.2 Page No: 167

1. Find the coordinates of the point which divides the join of (- 1, 7) and (4, – 3) in the ratio 2:3.

Let P(x, y) be the required point. Using the section formula, we get

x = (2×4 + 3×(-1))/(2 + 3) = (8 – 3)/5 = 1

y = (2×-3 + 3×7)/(2 + 3) = (-6 + 21)/5 = 3

Therefore, the point is (1, 3).

2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Let P (x 1 , y 1 ) and Q (x 2 , y2) be the points of trisection of the line segment joining the given points, i.e. AP = PQ = QB

Therefore, point P divides AB internally in the ratio 1:2.

x 1 = (1×(-2) + 2×4)/3 = (-2 + 8)/3 = 6/3 = 2

y 1 = (1×(-3) + 2×(-1))/(1 + 2) = (-3 – 2)/3 = -5/3

Therefore: P (x 1 , y 1 ) = P(2, -5/3)

Point Q divides AB internally in the ratio 2:1.

x 2 = (2×(-2) + 1×4)/(2 + 1) = (-4 + 4)/3 = 0

y 2 = (2×(-3) + 1×(-1))/(2 + 1) = (-6 – 1)/3 = -7/3

The coordinates of the point Q are (0, -7/3)

3. To conduct sports day activities in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the eighth line and posts a red flag. What is the distance between both flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

From the given instruction, we observed that Niharika posted the green flag at 1/4 th of the distance AD, i.e. (1/4 ×100) m = 25 m from the starting point of the 2nd line. Therefore, the coordinates of this point are (2, 25).

Similarly, Preet posted a red flag at 1/5 of the distance AD, i.e. (1/5 ×100) m = 20 m from the starting point of the 8th line. Therefore, the coordinates of this point are (8, 20).

Distance between these flags can be calculated by using the distance formula,

The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. Let’s say this point is P(x, y).

x = (2 + 8)/2 = 10/2 = 5 and y = (20 + 25)/2 = 45/2

Hence, P( x , y ) = (5, 45/2)

Therefore, Rashmi should post her blue flag at 45/2 = 22.5m on the 5th line.

4. Find the ratio in which the line segment joining the points (-3, 10) and (6, – 8) is divided by (-1, 6).

Consider the ratio in which the line segment joining (-3, 10) and (6, -8) is divided by point (-1, 6) be k :1.

Therefore, -1 = ( 6 k -3)/( k +1)

– k – 1 = 6 k -3

Therefore, the required ratio is 2: 7.

5. Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.

Let the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis be k:1. Therefore, the coordinates of the point of division, say P(x, y) is ((-4 k +1)/( k +1), (5 k -5)/( k +1)).

We know that the y-coordinate of any point on the x-axis is 0.

Therefore, ( 5k – 5)/(k + 1) = 0

So, the x -axis divides the line segment in the ratio 1:1.

Now, find the coordinates of the point of division:

P (x, y) = ((-4(1)+1)/(1+1) , (5(1)-5)/(1+1)) = (-3/2 , 0)

6. If (1, 2), (4, y ), ( x , 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y .

Let A, B, C and D be the points of a parallelogram: A(1, 2), B(4, y ), C( x , 6) and D(3, 5).

Since the diagonals of a parallelogram bisect each other, the midpoint is the same.

To find the value of x and y, solve for the midpoint first.

Midpoint of AC = ( (1+x)/2 , (2+6)/2 ) = ((1+x)/2 , 4)

Midpoint of BD = ((4+3)/2 , (5+y)/2 ) = (7/2 , (5+y)/2)

The midpoint of AC and BD are the same, this implies

(1+x)/2 = 7/2 and 4 = (5+y)/2

x + 1 = 7 and 5 + y = 8

x = 6 and y = 3

7. Find the coordinates of point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

Let the coordinates of point A be ( x , y ).

Mid-point of AB is (2, – 3), which is the centre of the circle.

Coordinate of B = (1, 4)

(2, -3) =((x+1)/2 , (y+4)/2)

(x+1)/2 = 2 and (y+4)/2 = -3

x + 1 = 4 and y + 4 = -6

x = 3 and y = -10

The coordinates of A(3,-10).

8. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

The coordinates of points A and B are (-2,-2) and (2,-4), respectively.

Since AP = 3/7 AB

Therefore, AP:PB = 3:4

Point P divides the line segment AB in the ratio 3:4.

9. Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Draw a figure, line dividing by 4 points.

From the figure, it can be observed that points X, Y, and Z are dividing the line segment in a ratio 1:3, 1:1, and 3:1, respectively.

10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4), and (-2,-1) taken in order.

[Hint: Area of a rhombus = 1/2 (product of its diagonals)

Let A(3, 0), B (4, 5), C( – 1, 4) and D ( – 2, – 1) are the vertices of a rhombus ABCD.

Exercise 7.3 Page No: 170

1. Find the area of the triangle whose vertices are:

(i) (2, 3), (-1, 0), (2, -4)

(ii) (-5, -1), (3, -5), (5, 2)

Area of a triangle formula = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )]

x 1 = 2, x 2 = -1, x 3 = 2, y 1 = 3, y 2 = 0 and y 3 = -4

Substitute all the values in the above formula, we get

Area of triangle = 1/2 [2 {0- (-4)} + (-1) {(-4) – (3)} + 2 (3 – 0)]

= 1/2 {8 + 7 + 6}

So, the area of the triangle is 21/2 square units.

x 1 = -5, x 2 = 3, x 3 = 5, y 1 = -1, y 2 = -5 and y 3 = 2

Area of the triangle = 1/2 [-5 { (-5)- (2)} + 3(2-(-1)) + 5{-1 – (-5)}]

= 1/2{35 + 9 + 20} = 32

Therefore, the area of the triangle is 32 square units.

2. In each of the following, find the value of ‘k’, for which the points are collinear.

(i) (7, -2), (5, 1), (3, -k)

(ii) (8, 1), (k, -4), (2, -5)

(i) For collinear points, the area of triangle formed by them is always zero.

Let points (7, -2), (5, 1), and (3, k) are vertices of a triangle.

Area of triangle = 1/2 [7 { 1- k} + 5(k-(-2)) + 3{(-2) – 1}] = 0

7 – 7k + 5k +10 -9 = 0

-2k + 8 = 0

(ii) For collinear points, the area of triangle formed by them is zero.

Therefore, for points (8, 1), (k, – 4), and (2, – 5), area = 0

1/2 [8 { -4- (-5)} + k{(-5)-(1)} + 2{1 -(-4)}] = 0

8 – 6k + 10 = 0

3. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Let the vertices of the triangle be A (0, -1), B (2, 1), and C (0, 3).

Let D, E, and F be the mid-points of the sides of this triangle.

Coordinates of D, E, and F are given by

D = (0+2/2, -1+1/2 ) = (1, 0)

E = ( 0+0/2, -1+3/2 ) = (0, 1)

F = ( 0+2/2, 3+1/2 ) = (1, 2)

Area of a triangle = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )]

Area of ΔDEF = 1/2 {1(2-1) + 1(1-0) + 0(0-2)} = 1/2 (1+1) = 1

The area of ΔDEF is 1 square unit

Area of ΔABC = 1/2 [0(1-3) + 2{3-(-1)} + 0(-1-1)] = 1/2 {8} = 4

The area of ΔABC is 4 square units

Therefore, the required ratio is 1:4.

4. Find the area of the quadrilateral whose vertices, taken in order, are

(-4, -2), (-3, -5), (3, -2) and (2, 3).

Let the vertices of the quadrilateral be A (- 4, – 2), B ( – 3, – 5), C (3, – 2), and D (2, 3).

Join AC and divide the quadrilateral into two triangles.

We have two triangles, ΔABC and ΔACD.

Area of ΔABC = 1/2 [(-4) {(-5) – (-2)} + (-3) {(-2) – (-2)} + 3 {(-2) – (-5)}]

= 1/2 (12 + 0 + 9)

= 21/2 square units

Area of ΔACD = 1/2 [(-4) {(-2) – (3)} + 3{(3) – (-2)} + 2 {(-2) – (-2)}]

= 1/2 (20 + 15 + 0)

= 35/2 square units

Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD

= (21/2 + 35/2) square units = 28 square units

5. You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC, whose vertices are A (4, – 6), B (3, – 2) and C (5, 2).

Let the vertices of the triangle be A (4, -6), B (3, -2), and C (5, 2).

Let D be the mid-point of side BC of ΔABC. Therefore, AD is the median in ΔABC.

Coordinates of point D = Midpoint of BC = ((3+5)/2, (-2+2)/2) = (4, 0)

Formula, to find area of a triangle = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )]

Now, a rea of ΔABD = 1/2 [(4) {(-2) – (0)} + 3{(0) – (-6)} + (4) {(-6) – (-2)}]

= 1/2 (-8 + 18 – 16)

= -3 square units

However, the area cannot be negative. Therefore, the area of ΔABD is 3 square units.

Area of ΔACD = 1/2 [(4) {0 – (2)} + 4{(2) – (-6)} + (5) {(-6) – (0)}]

= 1/2 (-8 + 32 – 30) = -3 square units

However, the area cannot be negative. Therefore, the area of ΔACD is 3 square units.

The area of both sides is the same. Thus, median AD has divided ΔABC into two triangles of equal areas.

Exercise 7.4 Page No: 171

1. Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, –2) and B(3, 7).

Consider line 2x + y – 4 = 0 divides line AB joined by the two points A(2, -2) and B(3, 7) in k:1 ratio.

Coordinates of point of division can be given as follows:

x = (2 + 3k)/(k + 1) and y = (-2 + 7k)/(k + 1)

Substituting the values of x and y given equation, i.e. 2x + y – 4 = 0, we have

2{(2 + 3k)/(k + 1)} + {(-2 + 7k)/(k + 1)} – 4 = 0

(4 + 6k)/(k + 1) + (-2 + 7k)/(k + 1) = 4

4 + 6k – 2 + 7k = 4(k+1)

-2 + 9k = 0

Hence, the ratio is 2:9.

2. Find the relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

If given points are collinear, then the area of the triangle formed by them must be zero.

Let (x, y), (1, 2) and (7, 0) are vertices of a triangle,

Area of a triangle = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )] = 0

2x – y + 7y – 14 = 0

2x + 6y – 14 = 0

x + 3y – 7 = 0.

Which is the required result.

3. Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).

Let A = (6, -6), B = (3, -7), and C = (3, 3) are the points on a circle.

If O is the centre, then OA = OB = OC (radii are equal)

If O = (x, y), then

OA = √[(x – 6) 2  + (y + 6) 2 ]

OB = √[(x – 3) 2  + (y + 7) 2 ]

OC = √[(x – 3) 2  + (y – 3) 2 ]

Choose: OA = OB, we have

After simplifying above, we get -6x = 2y – 14 ….(1)

Similarly, OB = OC

(x – 3) 2 + (y + 7) 2 = (x – 3) 2 + (y – 3) 2

(y + 7) 2 = (y – 3) 2

y 2 + 14y + 49 = y 2 – 6y + 9

Substituting the value of y in equation (1), we get

-6x = 2y – 14

-6x = -4 – 14 = -18

Hence, the centre of the circle is located at point (3,-2).

4. The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

Let ABCD is a square, where A(-1,2) and B(3,2). And Point O is the point of intersection of AC and BD.

To Find: Coordinate of points B and D.

Step 1: Find the distance between A and C and the coordinates of point O.

We know that the diagonals of a square are equal and bisect each other.

AC = √[(3 + 1) 2  + (2 – 2) 2 ] = 4

Coordinates of O can be calculated as follows:

x = (3 – 1)/2 = 1 and y = (2 + 2)/2 = 2

Step 2: Find the side of the square using the Pythagoras theorem

Let a be the side of the square and AC = 4

From the right triangle, ACD,

Hence, each side of the square = 2√2

Step 3: Find the coordinates of point D

Equate the length measure of AD and CD

Say, if the coordinates of D are (x 1 , y 1 )

AD = √[(x 1 + 1) 2  + (y 1 – 2) 2 ]

AD 2 = (x 1 + 1) 2  + (y 1 – 2) 2

Similarly, CD 2 = (x 1  – 3) 2  + (y 1 – 2) 2

Since all sides of a square are equal, which means AD = CD

(x 1 + 1) 2  + (y 1 – 2) 2 = (x 1  – 3) 2  + (y 1 – 2) 2

x 1 2 + 1 + 2x 1 = x 1 2 + 9 – 6x 1

The value of y 1 can be calculated as follows by using the value of x.

From step 2: each side of the square = 2√2

CD 2 = (x 1  – 3) 2  + (y 1 – 2) 2

8 = (1 – 3) 2  + (y 1 – 2) 2

8 = 4 + (y 1 – 2) 2

y 1 – 2 = 2

Hence, D = (1, 4)

Step 4: Find the coordinates of point B

From line segment, BOD

Coordinates of B can be calculated using coordinates of O, as follows:

Earlier, we had calculated O = (1, 2)

Say B = (x 2 , y 2 )

1 = (x 2 + 1)/2

And 2 = (y 2 + 4)/2

=> y 2 = 0

Therefore, the coordinates of required points are B = (1,0) and D = (1,4)

5. The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot, as shown in fig. 7.14. The students are to sow the seeds of flowering plants on the remaining area of the plot.

(i) Taking A as the origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of triangle PQR if C is the origin?

Also, calculate the areas of the triangles in these cases. What do you observe?

(i) Taking A as the origin, the coordinates of the vertices P, Q and R are,

From figure: P = (4, 6), Q = (3, 2), R (6, 5)

Here, AD is the x-axis and AB is the y-axis.

(ii) Taking C as the origin,

The coordinates of vertices P, Q and R are ( 12, 2), (13, 6) and (10, 3), respectively.

Here, CB is the x-axis and CD is the y-axis.

Find the area of triangles:

Area of triangle PQR in case of origin A:

Using formula: Area of a triangle = 1/2 × [x 1 (y 2 – y 3 ) + x 2 (y 3 – y 1 ) + x 3 (y 1 – y 2 )]

= ½ [4(2 – 5) + 3 (5 – 6) + 6 (6 – 2)]

= ½ (- 12 – 3 + 24 )

= 9/2 sq unit

(ii) Area of triangle PQR in case of origin C:

= ½ [ 12(6 – 3) + 13 ( 3 – 2) + 10( 2 – 6)]

= ½ ( 36 + 13 – 40)

This implies, Area of triangle PQR at origin A = Area of triangle PQR at origin C

The area is the same in both cases because the triangle remains the same no matter which point is considered as the origin.

6. The vertices of a ∆ ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E, respectively, such that AD/AB = AE/AC = 1/4. Calculate the area of the ∆ ADE and compare it with the area of ∆ ABC. (Recall Theorem 6.2 and Theorem 6.6)

Given: The vertices of a ∆ ABC are A (4, 6), B (1, 5) and C (7, 2)

AD/AB = AE/AC = 1/4

AD/(AD + BD) = AE/(AE + EC) = 1/4

Point D and Point E divide AB and AC, respectively, in ratio 1:3.

Coordinates of D can be calculated as follows:

x = (m 1 x 2 + m 2 x 1 )/(m 1 + m 2 ) and y = (m 1 y 2 + m 2 y 1 )/(m 1 + m 2 )

Here, m 1 = 1 and m 2 = 3

Consider line segment AB which is divided by point D at the ratio 1:3.

x = [3(4) + 1(1)]/4 = 13/4

y = [3(6) + 1(5)]/4 = 23/4

Similarly, the coordinates of E can be calculated as follows:

x = [1(7) + 3(4)]/4 = 19/4

y = [1(2) + 3(6)]/4 = 20/4 = 5

Find the area of triangle:

The area of triangle ∆ ABC can be calculated as follows:

= ½ [4(5 – 2) + 1( 2 – 6) + 7( 6 – 5)]

= ½ (12 – 4 + 7) = 15/2 sq unit

The area of ∆ ADE can be calculated as follows:

= ½ [4(23/4 – 5) + 13/4 (5 – 6) + 19/4 (6 – 23/4)]

= ½ (3 – 13/4 + 19/16)

= ½ ( 15/16 ) = 15/32 sq unit

Hence, the ratio of the area of triangle ADE to the area of triangle ABC = 1:16.

7. Let A (4, 2), B (6, 5), and C (1, 4) be the vertices of ∆ ABC.

(i) The median from A meets BC at D. Find the coordinates of point D.

(ii) Find the coordinates of the point P on AD such that AP:PD = 2:1.

(iii) Find the coordinates of points Q and R on medians BE and CF, respectively, such that BQ:QE = 2:1 and CR:RF = 2:1.

(iv) What do you observe?

[Note: The point which is common to all the three medians is called the centroid,

and this point divides each median in the ratio 2:1.]

(v) If A (x 1 , y 1 ), B (x 2 , y 2 ) and C (x 3 , y 3 ) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

(i) Coordinates of D can be calculated as follows:

Coordinates of D = ( (6+1)/2, (5+4)/2 ) = (7/2, 9/2)

So, D is (7/2, 9/2)

(ii) Coordinates of P can be calculated as follows:

Coordinates of P = ( [2(7/2) + 1(4)]/(2 + 1), [2(9/2) + 1(2)]/(2 + 1) ) = (11/3, 11/3)

So, P is (11/3, 11/3)

(iii) Coordinates of E can be calculated as follows:

Coordinates of E = ( (4+1)/2, (2+4)/2 ) = (5/2, 6/2) = (5/2 , 3)

So, E is (5/2, 3)

Points Q and P would be coincident because the medians of a triangle intersect each other at a common point called the centroid. Coordinate of Q can be given as follows:

Coordinates of Q =( [2(5/2) + 1(6)]/(2 + 1), [2(3) + 1(5)]/(2 + 1) ) = (11/3, 11/3)

F is the midpoint of the side AB

Coordinates of F = ( (4+6)/2, (2+5)/2 ) = (5, 7/2)

Point R divides the side CF in ratio 2:1

Coordinates of R = ( [2(5) + 1(1)]/(2 + 1), [2(7/2) + 1(4)]/(2 + 1) ) = (11/3, 11/3)

(iv) Coordinates of P, Q and R are the same, which shows that medians intersect each other at a common point, i.e. centroid of the triangle.

(v) If A (x 1 , y 1 ), B (x 2 , y 2 ) and C (x 3 , y 3 ) are the vertices of triangle ABC, the coordinates of the centroid can be given as follows:

x = (x 1 + x 2 + x 3 )/3 and y = (y 1 + y 2 + y 3 )/3

8. ABCD is a rectangle formed by the points A (-1, – 1), B (-1, 4), C (5, 4) and D (5, -1). P, Q, R and S are the midpoints of AB, BC, CD and DA, respectively. Is the quadrilateral PQRS a square, a rectangle or a rhombus? Justify your answer.

P id the midpoint of side AB,

Coordinate of P = ( (-1 – 1)/2, (-1 + 4)/2 ) = (-1, 3/2)

Similarly, Q, R and S are (As Q is the midpoint of BC, R is the midpoint of CD and S is the midpoint of AD)

Coordinate of Q = (2, 4)

Coordinate of R = (5, 3/2)

Coordinate of S = (2, -1)

Length of PQ = √[(-1 – 2) 2 + (3/2 – 4) 2 ] = √(61/4) = √61/2

Length of SP = √[(2 + 1) 2 + (-1 – 3/2) 2 ] = √(61/4) = √61/2

Length of QR = √[(2 – 5) 2 + (4 – 3/2) 2 ] = √(61/4) = √61/2

Length of RS = √[(5 – 2) 2 + (3/2 + 1) 2 ] = √(61/4) = √61/2

Length of PR (diagonal) = √[(-1 – 5) 2 + (3/2 – 3/2) 2 ] = 6

Length of QS (diagonal) = √[(2 – 2) 2 + (4 + 1) 2 ] = 5

The above values show that PQ = SP = QR = RS = √61/2, i.e. all sides are equal.

But PR ≠ QS, i.e. diagonals are not of equal measure.

Hence, the given figure is a rhombus.

This chapter comes under Unit-Coordinate Geometry and has a weightage of 6 marks in the board examination. There will be one mark MCQ questions, 2 marks reasoning questions, and 3 marks short answer questions. This chapter has fundamental concepts that lay the foundation for your future studies.

Sub-topics of Class 10 Chapter 7 Coordinate Geometry

• Introduction to Coordinate Geometry
• Distance Formula
• Section Formula
• Area of the Triangle

List of Exercises from Class 10 Maths Chapter 7 Coordinate Geometry

Exercise 7.1 – 10 Questions, which includes 8 practical-based questions, 2 reasoning questions Exercise 7.2 – 10 Questions, which includes 8 long answer questions, 2 short answer questions Exercise 7.3 – 5 Questions, which includes 3 long answer questions, 2 practical-based questions Exercise 7.4 – 8 Questions, which includes 6 long answer questions, 1 practical-based question, 1 reasoning question

NCERT Solutions are carefully drafted to assist the student in scoring good marks in the examination. It provides you with much-needed problem-solving practice.

This chapter deals with finding the area between two points whose coordinate values are provided. For instance, the area of a triangle. This chapter has some basic concepts like the area of a triangle, rhombus, the distance between sides, and intersections. This chapter teaches you the relationship between numerical and geometry and their application in our daily lives.

These  NCERT Solutions for Class 10 Maths have different types of questions and their answers which will help you with alternate solutions and diagrammatic representation. The solutions provided here are written in simple language with apt information. By studying these NCERT Solutions thoroughly, students will be able to solve complex problems easily.

Key Features of NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

• The solution has all the exercise questions provided in the NCERT textbook.
• Diagrammatic representations and alternate methods will help you understand the concepts thoroughly.
• Solving these NCERT Solutions will make you acquainted with important formulas and standards.
• This NCERT Solution has different examples that will help you relate to real-life examples to relate geometry and numerical.

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To provide students with more problems for practice, we at BYJU’S also provide solutions for other textbooks which can be accessed absolutely free of cost.

• RD Sharma Solutions for Class 10 Maths Chapter 14 Coordinate Geometry

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Dropped Topics –  7.4 Area of a triangle

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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)

CBSE's question bank on case study for Class 10 Maths Chapter 7 is available here. Practice this new type of questions to score good marks in your board exam.

Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry

CASE STUDY 1:

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.

1. Find the position of green flag

b) (2,0.25)

d) (0, -25)

Answer:   a) (2,25)

2. Find the position of red flag

Answer:  c) (8,20)

3. What is the distance between both the flags?

a) √41

b) √11

c) √61

d) √51

Answer:  c) √61

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

d) (2.5,20)

Answer:  a) (5, 22.5)

5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

Answer:  a) (3.5,24)

CASE STUDY 2:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer:  a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer:  c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer:  d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer:  a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer:  d) 4.5

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

CBSE Sample Papers For Class 10 & 12

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Case Study Questions Class 10 Science Control and Coordination

Case study questions class 10 science chapter 7 control and coordination.

CBSE Class 10 Case Study Questions Science Control and Coordination. Important Case Study Questions for Class 10 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Control and Coordination.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Based Questions Class 10 Science Biology Chapter 7

Case study : 1.

If the body design in the squirrel relied only on electrical impulses via nerve cells, the range of tissues instructed to prepare for the coming activity would be limited. On the other hand, if a chemical signal were to be sent as well, it would reach all cells of the body and provide the wideranging changes needed. This is done in many animals, including human beings, using a hormone called adrenaline that is secreted from the adrenal glands.

i) which is the target organ for the adrenaline hormone?

Ans: Heart is the target organ for the adrenaline hormone which increases the heartbeat rate.

ii) Which hormone is released by thyroid gland?

Ans: Thyroxine is released by thyroid gland.

iii) What is the function of thyroxine hormone?

Ans: It regulates carbohydrate, protein and fat metabolism in the body and promote the best balance for growth.

iv) Name the hormone released by ovary?

Ans: Estrogen and progesterone

V) Name the three hormonal glands located in the brain?

Ans: Pineal, pituitary and hypothalamus

CASE STUDY : 2

Some plants like the pea plant climb up other plants or fences by means of tendrils. These tendrils are sensitive to touch. When they come in contact with any support, the part of the tendril in contact with the object does not grow as rapidly as the part of the tendril away from the object. This causes the tendril to circle around the object and thus cling to it. More commonly, plants respond to stimuli slowly by growing in a particular direction. Because this growth is directional, it appears as if the plant is moving.

i) How many type of tropism are shown by plants? Name them.

Ans: Generally there are 6 type of tropism namely phototropism, gravitropism, chemotropism, thigmotropism, thermotropism and hydrotropism.

ii) The touch me not plant is an example of which tropism?

Ans: it is an example of thigmotropism.

iii) give one example of chemotropism?

Ans: growth of pollen tubes to wheels is one example of chemotropism.

iv) Name the plants hormone which promotes cell division?

Ans: Cytokinins promotes cell division in plants.

v) Name the plant hormone which inhibits growth?

Ans: Abscisic acid

CASE STUDY : 3

We also think about our actions. Writing, talking, moving a chair, clapping at the end of a programme are examples of voluntary actions which are based on deciding what to do next. So, the brain also has to send messages to muscles. This is the second way in which the nervous system communicates with the muscles. The communication between the central nervous system and the other parts of the body is facilitated by the peripheral nervous system consisting of cranial nerves arising from the brain and spinal nerves arising from the spinal cord. The brain thus allows us to think and take actions based on that thinking.

i) what are the three major parts of the brain?

Ans: Forebrain, Midbrain and hindbrain.

ii) what are the function of medulla?

Ans: It controls all the involuntary action such as blood pressure, salivation, vomiting, etc.

iii) Which fluid is present in our brain?

Ans: Cerebrospinal fluid.

iv) What is the function of hypothalamus?

Ans: It regulates homeostasis, releases hormones.

v) What is the function of mid brain?

Ans: The mid brain connects the forebrain and hindbrain.

CASE STUDY : 4

Body consists of dense networks of intricately arranged neurons. It sits in the forward end of the skull, and receives signals from all over the body which it thinks about before responding to them. Obviously, in order to receive these signals, this thinking part of the brain in the skull must be connected to nerves coming from various parts of the body.

i) What is reflex?

Ans: It is the sudden action done in response to something in the environment.

ii) How does the nervous tissue cause action?

Ans: When a nerve impulse  reaches the muscles, the muscles fibres move by changing their shape and their arrangements in the cell.

iii) What is the function of the motor neuron?

Ans: It transmits the impulses from spinal cord to skeletal muscles.

iv) What is reflex arc?

Ans: It is the neural pathway that controls reflex starting from a sensory neuron and end at effector.

v) What is the role of sensory neuron?

Ans: It carry signals from outer part of body to central nervous system.

CASE STUDY : 5

In animals, such control and coordination are provided by nervous and muscular tissues. Touching a hot object is an urgent and dangerous situation for us. We need to detect it, and respond to it. How do we detect that we are touching a hot object? All information from our environment is detected by the specialised tips of some nerve cells. These receptors are usually located in our sense organs, such as the inner ear, the nose, the tongue, and so on. So gustatory receptors will detect taste while olfactory receptors will detect smell.

i) What are the parts of neuron?

Ans: Dendrite, nucleus, axon, nerve ending and a cell body.

ii) Which part of neuron receive the information first?

Ans: Dendritic tip receive the information first.

iii)  At which place the electrical impulse get converted to a chemical impulse?

Ans: At synapse or a gap between nerve ending and a dendritic tip.

iv) What is neuromuscular junction?

Ans: The neuromuscular is made up of two words neuron & muscles, so it is the place where neuron and muscle fibre meet.

v) Draw the picture of neuron?

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Case Study Class 10

If you are looking for the CBSE Case Study class 10 Questions in PDF, then you are in the right place. CBSE 10th Class Case Study for the Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study or passage.

CBSE Board will be asking case study questions based on subjects in the upcoming board exams. Thus, it becomes an essential resource to study. 

The Case Study Class 10 Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.

Download Class 10 Case Study Questions and Answers PDF Subject Wise

Download links of class 10 Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.

Class 10 Case Study Questions for Science

Class 10 case study questions for maths.

• Class 10 Case Study Questions for English

Class 10 Case Study Questions for Social Science

Students are advised to access Case Study questions class 10 CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 questions.

CBSE Class 10 Case Study Questions for Maths is one of the best ways to prepare for the exam. Because the format of Maths Case Study questions are very similar to the MCQ types questions. We have CBSE Class 10 MCQ Questions as well, students can also download them.

The Case Based Question of Maths will enable the students to gain in-depth knowledge of all kinds of theorems and formulas. The case study questions we are providing here are prepared by subject matter experts.

Meaning solving the case study maths question for class 10th will allow the students to enhance their accuracy and manage the time to answer case study questions.

Hopefully, you have found some useful and relevant study resources here. Feel free to download Class 10 Case Study Questions for Maths that include all kinds of resources at the same place. All are free of cost and available in PDF file.

Case Study Questions Class 10 Chapter 1 Real Numbers

Case Study Questions Class 10 Chapter 2 Polynomials

Case Study Questions Class 10 Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Chapter 4 Quadratic Equations

Case Study Questions Class 10 Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Chapter 6 Triangles

Case Study Questions Class 10 Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Chapter 10 Circles

Case Study Questions Class 10 Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Chapter 14 Statistics

Case Study Questions Class 10 Chapter 15 Probability

Class 10 Case Study Questions Chapter Wise for Science will help a lot in exams. Practicing the Case study question from every single chapter will aid the students to do a qualitative research of chapters and topics.

Doing this will arouse interest in subjects. Chapter wise Case Study Questions can be very beneficial to the students if they solve it regularly.

It will help the students to get to know about their weaknesses and strengths in the chapters. Therefore we have composed the chapter wise Class 10 Case Study Questions for Science. Students can download them here.

Case Study Questions Class 10 Science Chapter 1 Chemical Reactions & Equations

Case Study Questions Class 10 Science Chapter 2 Acids, Bases & Salts

Case Study Questions Class 10 Science Chapter 3 Metals & Non-metals

Case Study Questions Class 10 Science Chapter 4 Carbon & Its Compounds

Case Study Questions Class 10 Science Chapter 5 Periodic Classification of Elements

Case Study Questions Class 10 Science Chapter 6 Life Processes

Case Study Questions Class 10 Science Chapter 8 How Do Organisms Reproduce

Case Study Questions Class 10 Science Chapter 9 Heredity & Evolution

Case Study Questions Class 10 Science Chapter 10 Light-Reflection & Refraction

Case Study Questions Class 10 Science Chapter 11 The Human Eye & the Colourful World

Case Study Questions Class 10 Science Chapter 12 Electricity

Case Study Questions Class 10 Science Chapter 13 Magnetic Effects of Electric Current

Case Study Questions Class 10 Science Chapter 15 Our Environment

Case Study Questions Class 10 Social Science Chapter Wise PDF can be downloaded here for free of cost. The Social Science Case study questions for class 10th help the students to cover the critical core concepts of Social Science subjects.

Social Science case study consists of passage based questions in which students need to read the paragraph and answer the given questions.

Answering the questions that are given below the passage will be required to have detailed analysis of the passage. Class 10 Social Science has various chapters and that passage can be from any chapter of Social Science subject.

Therefore, students should have a better grasp over the CBSE Class 10 Social Science subjects. Students willing to score better marks will not leave any stone unturned. That’s why they will practice solving the Case Study Questions Class 10 Social Science.

Case Study Questions Class 10 Social Science India And the Contemporary World - II

Case Study Questions Class 10 Social Science Contemporary India - II

Case Study Questions Class 10 Social Science Democratic Politics - II

Case Study Questions Class 10 Social Science Understanding Economic Development

How to Solve Case Study Based Questions Class 10 ?

In order to solve the Case Study Based Questions Class 10 students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them. 

While solving the class 10 Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers. 

Case Study class 10 consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.

Also, before solving the Case study type questions it is ideal to use the CBSE Syllabus to brush up the previous learnings.

Features Of Class 10 Case Study Questions And Answers Pdf

Students referring to the Class 10 Case Study Questions And Answers Pdf from Selfstudys will find these features:-

• Accurate answers of all the Case-based questions given in the PDF.
• Case Study class 10 solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
• Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.

Benefits of Using CBSE Class 10 Case Study Questions and Answers

Since, CBSE Class 10 Case Study Questions and Answers are prepared by our experts referring to the CBSE Class 10 Syllabus, it provided benefits in various way:-

• Case study class 10 helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
• It allows students to utilise their learning to solve real life problems.
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• Those students who solve Case Study Class 10 on a regular basis become extremely good at answering normal formula based questions.
• By using class 10 Case Study questions and answers pdf, students focus more on Selfstudys instead of wasting their valuable time.
• With the help of given solutions students learn to solve all Case Study questions class 10 CBSE chapter wise pdf regardless of its difficulty level.

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Case Study Questions Class 10 Geography -Lifelines of National Economy

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Case study Questions on Class 10 Social Science Geography Chapter 7  are very important to solve for your exam. Class 10 Social Science Chapter 7 Case Study Questions Class 10 Geography has been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Social Science Chapter 7 Lifelines of National Economy

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In CBSE Class 10 Social Science Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Lifelines of National Economy Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Social Science  Chapter 7 Lifelines of National Economy

Case Study/Passage-Based Questions

Case Study 1: Railways are the principal mode of transportation for freight and passengers in India. Railways also make it possible for people to conduct multifarious activities like business, sightseeing, pilgrimage along with transportation of goods over longer distances. Apart from being an important means of transport, the Indian Railways have been a great integrating force for more than 150 years. Railways in India bind the economic life of the country as well as accelerate the development of industry and agriculture. The Indian Railway is now reorganised into 16 zones. The distribution pattern of the Railway network in the country has been largely influenced by physiographic, economic, and administrative factors. The Northern plains with their vast level, high population density, and rich agricultural resources provided the most favorable condition for their growth. However, a large number of rivers requiring the construction of bridges across their wide beds posed some obstacles. In the hilly terrains of the peninsular region, railway tracts are laid through low hills, gaps or tunnels

(i) Which of the following factors are responsible for distribution pattern of railways network in the country? Identify the correct option: (a) Topographical factors (b) Economic and administrative factors (c) Social factors (d) Both (a) and (b)

Answer: (d) Both (a) and (b)

(ii) Assertion (A): Rail Transport is the most convenient means of transportation in the Northern Plains. Reason (R): The Northern Plains are densely populated, which enables the maximum number of people to utilize this means of transport. Codes (a) Both A and R are true and R is the correct explanation of A (b) Both A and Rare true, but R is not the correct explanation of A (c) A is true, but R is false (d) A is false, but R is true

Answer: (a) Both A and R are true and R is the correct explanation of A

(iii) When was the first railway line opened in India? (a) 1803 (b) 1823 (c) 1853 (d) 1854

Answer: (c) 1853

(iv) Why Indian railway network is mostly concentrated in Ganga Plains? (a) Due to concentration of Industries. (b) Due to topographical uniformity and high density of population. (c) Due to high agricultural production. (d) Due to lack of economic opportunities.

Answer: (b) Due to topographical uniformity and high density of population.

Why are the Indian Railways called the lifeline of the country? (a) Railways in India bind the economic life of the country. (b) It is the largest public undertaking in the country. (c) Railways are the principal mode of transportation for freight and passengers in India. (d) All of the above

Answer: (d) All of the above

(vi) Why is it essential to develop a unigauge system of railways in our country? (a) It will lead to a reduction in trans-shipment. (b) Because it has a larger capacity. (c) Both (a) and (b) (d) It will bring administrative convenience.

Answer: (c) Both (a) and (b)

Case Study 2: The chapter “Lifelines of National Economy” in Class 10 Geography focuses on the transportation network and its crucial role in connecting various regions and supporting economic activities. It explores different modes of transportation, including roadways, railways, waterways, and airways, and their significance in the movement of goods, people, and services. The chapter discusses the development of transportation infrastructure, such as the Golden Quadrilateral, dedicated freight corridors, and national waterways. It also highlights the challenges faced in transportation, such as inadequate infrastructure, congestion, and environmental concerns. Additionally, the chapter examines the role of communication networks, including the internet, in facilitating trade, commerce, and connectivity.

Which chapter in Class 10 Geography focuses on the transportation network?

a) Chapter 2: Forests and Wildlife Resources

b) Chapter 4: Agriculture

c) Chapter 7: Minerals and Energy Resources

d) Chapter 10: Lifelines of National Economy

Answer: d) Chapter 10: Lifelines of National Economy

What are the different modes of transportation discussed in the chapter?

a) Only roadways and railways

b) Only waterways and airways

c) Only railways and airways

d) Roadways, railways, waterways, and airways

Answer: d) Roadways, railways, waterways, and airways

What is the significance of transportation in the economy?

a) It has no impact on economic activities.

b) It facilitates the movement of goods, people, and services.

c) It hinders economic development.

d) It promotes environmental conservation.

Answer: b) It facilitates the movement of goods, people, and services.

What are some of the challenges faced in transportation?

a) Adequate infrastructure and efficient connectivity

b) Lack of congestion and environmental concerns

c) Inadequate infrastructure, congestion, and environmental concerns

d) High speed and seamless connectivity

Answer: c) Inadequate infrastructure, congestion, and environmental concerns

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Social Science Geography Chapter 7 Lifelines of National Economy Resources with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Social Science Lifelines of National Economy Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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