NCERT Mathematics · Class 10 · English · 2026-27

Coordinate Geometry — Exercise 7.2

Independently written, step-by-step solutions. Prompts below are concise paraphrases; use the official textbook for the complete question wording.

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Question 1

Divide the segment from (−1,7) to (4,−3) internally in ratio 2:3.

Step-by-step solution

Use the section formula with m=2,n=3. x=[2×4+3(−1)]/5=1; y=[2(−3)+3×7]/5=3.

\[P=\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right),\quad AP:PB=m:n\]

Answer: (1,3).

Resource ID: CB-10-M-CH7-EX7.2-Q1

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Question 2

Find the trisection points between (4,−1) and (−2,−3).

Step-by-step solution

The displacement from A to B is (−6,−2). Add one third and two thirds of this displacement to A: P=(4−2,−1−2/3); Q=(4−4,−1−4/3).

Answer: (2,−5/3) and (0,−7/3).

Resource ID: CB-10-M-CH7-EX7.2-Q2

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Question 3

Find the flag separation and halfway position in the sports-ground model.

Step-by-step solution

Take A as origin, line number as x and distance along AD as y, in metres. The green flag is G(2,25), and red flag R(8,20). GR=√[(8−2)²+(20−25)²]=√61 m. The midpoint is ((2+8)/2,(25+20)/2).

Answer: Distance √61 m; blue flag at (5,22.5), on the fifth line and 22.5 m from AB.

Resource ID: CB-10-M-CH7-EX7.2-Q3

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Question 4

Find the internal ratio in which (−1,6) divides (−3,10) to (6,−8).

Step-by-step solution

Let ratio be k:1. Then −1=(6k−3)/(k+1), so −k−1=6k−3 and 7k=2. Thus k=2/7. Check y=(2(−8)+7×10)/9=6.

Answer: 2:7.

Resource ID: CB-10-M-CH7-EX7.2-Q4

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Question 5

Find where the x-axis divides A(1,−5) to B(−4,5), including the ratio.

Step-by-step solution

A point on the x-axis has y=0. The section formula gives 0=(5m−5n)/(m+n), hence m=n. It is the midpoint; x=(1−4)/2=−3/2.

Answer: Ratio 1:1; point (−3/2,0).

Resource ID: CB-10-M-CH7-EX7.2-Q5

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Question 6

Find x,y for the parallelogram (1,2),(4,y),(x,6),(3,5), in order.

Step-by-step solution

Diagonals of a parallelogram have the same midpoint. Their coordinate sums therefore agree: (1+x,2+6)=(4+3,y+5). So 1+x=7 and 8=y+5.

Answer: x=6, y=3.

Resource ID: CB-10-M-CH7-EX7.2-Q6

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Question 7

A circle has centre (2,−3), and diameter endpoint B(1,4). Find the other endpoint A.

Step-by-step solution

The centre is the midpoint of diameter AB. Thus (x+1)/2=2 and (y+4)/2=−3. Solve x+1=4 and y+4=−6.

Answer: A=(3,−10).

Resource ID: CB-10-M-CH7-EX7.2-Q7

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Question 8

For A(−2,−2), B(2,−4), find P on AB with AP=3AB/7.

Step-by-step solution

Since PB=4AB/7, AP:PB=3:4. Then x=[3×2+4(−2)]/7=−2/7 and y=[3(−4)+4(−2)]/7=−20/7.

Answer: P=(−2/7,−20/7).

Resource ID: CB-10-M-CH7-EX7.2-Q8

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Question 9

Divide A(−2,2) to B(2,8) into four equal segments.

Step-by-step solution

The full displacement is (4,6). One quarter is (1,3/2). Add this once, twice and three times to A.

Answer: (−1,7/2), (0,5), (1,13/2).

Resource ID: CB-10-M-CH7-EX7.2-Q9

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Question 10

Find the area of the rhombus (3,0),(4,5),(−1,4),(−2,−1), in order.

Step-by-step solution

AC=√[(−1−3)²+(4−0)²]=√32=4√2. BD=√[(−2−4)²+(−1−5)²]=√72=6√2. Rhombus area is half the product of diagonals.

Answer: Area=(1/2)(4√2)(6√2)=24 square units.

Resource ID: CB-10-M-CH7-EX7.2-Q10

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