NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2 focus on the section formula in coordinate geometry. This exercise will help you find the coordinates of a point that divides a line segment in a given ratio, which is an important concept in the CBSE Class 10th syllabus.
These NCERT Solutions are explained in a clear step-by-step manner, making it easier for you to understand how formulas are applied to different types of problems. Practising these questions improves accuracy and strengthens your understanding of coordinate geometry concepts.
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2
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,
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.
Therefore P(x 1 ,y 1 ) = (2, -5/3)
Point Q divides AB internally in the ratio 2:1.
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?
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 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 the y-coordinate of any point on the 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 a circle whose centre is (2, - 3) and B is (1, 4).
Answer:
Let ( x , y ) be the coordinate of A. Since A B is the diameter of the circle, the centre will be the mid-point of A B .
Now, as centre is the mid-point of A B . x -coordinate of centre = (2 x + 1)/2 y -coordinate of centre = (2 y + 4)/2
But given that centre of circle is ( 2 , − 3 ) .
Therefore, (2 x + 1)/2 = 2 ⇒ x = 3 (2 y + 4 )/2 = − 3 ⇒ y = − 1 0 Thus the coordinate of A is ( 3 , − 1 0 ) .
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 A P = 3/7 A B
∴ B P = 4/7
Then, ratio of A P and P B = m 1 : m 2 = 3 : 4
Let the coordinates of P be ( x , y ) .
∴ x = (m 1 x 2 + m 2 x 1 ) / ( m 1 + m 2 )
⇒ x = ( 3 × 2 + 4 × ( −2 )) / (3 + 4) = ( 6 − 8) / 7 = −2 / 7
And y = (m 1 y 2 + m 2 y 1 ) / ( m 1 + m 2 )
⇒ y = ( (3 × ( −4 ) + 4 × ( −2 )) / (3 + 4) = (−12 − 8) / 7 = −20 / 7
∴ Coordinates of P = −2 / 7 , −20 / 7
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
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.
How to Score Better in Class 10 Maths Exam?
Scoring well in Class 10 Maths requires clear concepts, regular practice, and a focus on accuracy and answer presentation. To score better, you should:
Focus on understanding concepts in Class 10 Maths instead of memorising steps, as this helps in solving application-based questions.
Focus on difficult topics from the Class 10 Maths syllabus instead of skipping them to avoid losing marks.
Regular revision of PW Class 10 Maths MIQs helps avoid calculation mistakes in exams.
Solve all CBSE Class 10 NCERT questions multiple times to strengthen your basics and improve accuracy.
Practising CBSE Class 10 Maths previous year questions (PYQs) helps you understand question patterns and important topics.
Explore More Chapters
.png)
.png)
.png)
.png)
.png)
.png)
