NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2
Get detailed NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 on Coordinate Geometry. Learn how to calculate the area of a triangle using the coordinate geometry formula with step-by-step explanations and solutions.
Ananya Gupta8 Jan, 2025
Share
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2: NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 help students to understand important concepts related to coordinate geometry. This exercise focuses on the section of the chapter where students learn how to find the area of a triangle using the coordinate geometry formula.
By solving these problems, students can strengthen their understanding of how coordinates work in geometry, enhancing their ability to solve problems in competitive exams and improve their conceptual clarity.Important Questions for Class 10 Maths Chapter 7
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 Overview
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 focuses on finding the area of a triangle when the coordinates of its three vertices are given. In this exercise, students learn how to apply the coordinate geometry formula for calculating the area of a triangle using the determinant method. The exercise provides various problems that guide students step by step to understand the application of the formula.NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 PDF
The NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 are created to help students understand the concept of finding the area of a triangle when the coordinates of its vertices are known.CBSE Class 10 Maths Sample Paper 2024-25
This exercise provides detailed solutions that guide students through the step-by-step process of applying the coordinate geometry formula. To access the solutions in PDF format, the link is available below, allowing students to download and use it for their practice and reference.NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 PDF
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2
Solve the followings Questions.
1. Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.Answer:
Let P(x, y) be the required point. Using the section formula.png)
.png)
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).
Answer:
.png)
Let P (x
1
,y
1
) and Q (x
2
,y
2
) are 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.
.png)
.png)
Therefore P(x
1
,y
1
) = (2, -5/3)
Point Q divides AB internally in the ratio 2:1.
.png)
.png)
Q (x
2
,y
2
) = (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 the flags? If Rashmi has to post a blue flagexactly halfway between the line segment joining the two flags, where should she post her flag?
Answer:
.png)
4. Find the ratio in which the line segment joining the points (-3, 10) and (6, - 8) is divided by (-1, 6).
Answer:
Let the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k:1. Therefore, -1 = 6k-3/k+1 -k - 1 = 6k -3 7k = 2 k = 2/7 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.Answer:
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axis be k:1. Therefore, the coordinates of the point of division is (-4k+1/k+1, 5k-5/k+1). We know that y-coordinate of any point on x-axis is 0. ∴ 5k-5/k+1 = 0 Therefore, x-axis divides it in the ratio 1:1. To find the coordinates let's substitute the value of k in equation(1) Required point = [(- 4(1) + 1) / (1 + 1), (5(1) - 5) / (1 + 1)] = [(- 4 + 1) / 2, (5 - 5) / 2] = [- 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.Answer:
Let A,B,C and D be the points (1,2) (4,y), (x,6) and (3,5) respectively.
7. Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).
Answer:
Let be the coordinate of . Since is the diameter of the circle, the centre will be the mid-point of . now, as centre is the mid-point of . -coordinate of centre -coordinate of centre But given that centre of circle is . Therefore, Thus the coordinate of is . 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.Answer:
As given the coordinates of A(−2,−2) and B(2,−4) and P is a point lies on AB. And
Then, ratio of
and
Let the coordinates of
be
.
And
Coordinates of
9. Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.
Answer:
From the figure, it can be observed that points X,Y,Z are dividing the line segment in a ratio 1:3,1:1,3:1 respectively.
Using Sectional Formula, we get,
Coordinates of X = ((1 × 2 + 3 × (−2)) / (1 + 3), (1 × 8 + 3 × 2) / (1 + 3))
= (−1, 7/2)
Coordinates of Y = (2 − 2) / 2, (2 + 8) / 2 = (0,5)
Coordinates of Z = ((3 × 2 + 1 × (−2)) / (1 + 3), (3 × 8 + 1 × 2) / (1 + 3)
= (1, 13/2)
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)]
Answer:
Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B, C, D of a rhombus ABCD. Length of the diagonal AC=
Length of the diagonal BD=
.png)
Area of rhombus ABCD = 1/2 X 4√2 X 6√2= 24 square units.
Therefore, the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is 24 square units.
Benefits of Solving NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2
- Concept Clarity : The exercise helps students grasp the concept of coordinate geometry, particularly focusing on finding the area of a triangle when the coordinates of its vertices are given. Understanding these concepts is essential for solving real-life problems.
- Step-by-Step Solutions : The solutions are broken down into simple steps, making it easier for students to understand and apply formulas correctly. This approach boosts their confidence and problem-solving skills.
- Improves Accuracy : Practice with this exercise enhances accuracy in applying formulas for calculating areas and understanding geometric properties of figures in coordinate geometry.
- Helps in Exam Preparation : By practicing these problems, students can strengthen their foundation for upcoming exams and improve their performance in both school assessments and competitive exams.
- Boosts Problem-Solving Skills : The exercise challenges students to think analytically and solve problems by applying the concepts learned, fostering critical thinking and problem-solving skills.
- Time Management : Regular practice helps students manage time efficiently, enabling them to attempt questions with speed and accuracy during exams.
- Confidence Building : As students practice and solve a variety of problems, they gain more confidence in their ability to tackle similar questions in exams, reducing exam anxiety.
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 FAQs
What is the main focus of Exercise 7.2 in Chapter 7?
Exercise 7.2 focuses on the application of the coordinate geometry concepts to find the area of a triangle when the coordinates of its vertices are given. This exercise helps students understand how to use the area formula for a triangle in coordinate geometry.
Why is this exercise important for Class 10 students?
This exercise is crucial as it helps students develop a strong understanding of coordinate geometry, which is an important topic in Class 10 Maths. It also improves problem-solving skills and prepares students for exams by reinforcing important formulas and concepts.
Can I use the formula for the area of a triangle directly without checking the coordinates?
It's important to first ensure that the coordinates provided are correct and represent a valid triangle. Always double-check the values before applying the formula to avoid calculation errors.
Is Exercise 7.2 important for exams?
Yes, problems related to finding the area of a triangle in coordinate geometry are often included in exams. Mastering this exercise will help you tackle such questions efficiently.
🔥 Trending Blogs
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Check out these Related Articles
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.