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Coordinate Geometry Class 10 Maths Chapter 7 Exercise 7.2 PDF

The Coordinate Geometry Class 10 Maths Chapter 7 Exercise 7.2 PDF helps students learn how to calculate the area of a triangle using coordinate formulas. With clear steps and practice questions, it strengthens geometry concepts and improves accuracy. Ideal for revising coordinate geometry exercise 7.2 solutions.
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Coordinate Geometry Class 10 Exercise 7.2: Class 10 Maths Chapter 7 Exercise 7.2 introduces students to practical applications of dividing line segments in coordinate geometry, building directly on the previous exercise's concepts.

This exercise contains 10 questions with 5 supporting examples, progressing from basic internal division problems to more challenging ones involving external division, midpoints, and verifying ratios or collinearity of points.  

Questions like finding coordinates of points dividing joins in simple ratios, determining ratios from given points, or solving real-life scenarios such as path division help develop analytical skills essential for board exams, where Q2, 5, 8, and 9 often pose greater difficulty requiring careful visualisation through sketches.

Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 Solutions 

Below are the NCERT Solutions for Class 10 Maths Coordinate Geometry Exercise 7.2, designed to help students understand and apply the area of a triangle formula using coordinates. These step-by-step solutions make problem-solving easier and strengthen conceptual clarity in coordinate geometry.

Solve the following 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,
 chapter 7-Coordinate Geometry Exercise 7.2/18.PNG
  chapter 7-Coordinate Geometry Exercise 7.2/18.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:

chapter 7-Coordinate Geometry Exercise 7.2/18.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.
 chapter 7-Coordinate Geometry Exercise 7.2/18.PNG
chapter 7-Coordinate Geometry Exercise 7.2/18.PNG
Therefore P(x  1 ,y 1 ) = (2, -5/3) Point Q divides AB internally in the ratio 2:1.
 chapter 7-Coordinate Geometry Exercise 7.2/18.PNG
chapter 7-Coordinate Geometry Exercise 7.2/18.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 flag exactly halfway between the line segment joining the two flags, where should she post her flag?  math 10

Answer:

chapter 7-Coordinate Geometry Exercise 7.2/18.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 the 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. chapter 7-Coordinate Geometry Exercise 7.2/fig-2.jpg


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:

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:

chapter 7-Coordinate Geometry Exercise 7.2/fig-4.PNG
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
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.

Class 10 Maths Coordinate Geometry Chapter Exercise 7.2

Exercise 7.2 helps students understand how to calculate the area of a triangle using the coordinate geometry formula. It strengthens analytical skills by teaching how coordinates determine geometric shapes on the Cartesian plane.

A clear, step-by-step solution PDF is provided to make concepts easier, support quick revision, and help students confidently prepare for Coordinate Geometry Class 10 Exercise 7.2 and upcoming exams.

Class 10 Maths Coordinate Geometry Chapter Exercise 7.2

NCERT Solutions for Class 10 Maths Chapter 1 NCERT Solutions for Class 10 Maths Chapter 9
NCERT Solutions for Class 10 Maths Chapter 2 NCERT Solutions for Class 10 Maths Chapter 10
NCERT Solutions for Class 10 Maths Chapter 3 NCERT Solutions for Class 10 Maths Chapter 11
NCERT Solutions for Class 10 Maths Chapter 4 NCERT Solutions for Class 10 Maths Chapter 12
NCERT Solutions for Class 10 Maths Chapter 5 NCERT Solutions for Class 10 Maths Chapter 13
NCERT Solutions for Class 10 Maths Chapter 6 NCERT Solutions for Class 10 Maths Chapter 14
NCERT Solutions for Class 10 Maths Chapter 7 NCERT Solutions for Class 10 Maths Chapter 15
NCERT Solutions for Class 10 Maths Chapter 8  

Class 10 Maths Coordinate Geometry Chapter 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.
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