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Question

What is the ratio in which P(2,5) divides the line joining the points (8,2) and (6,9)?

A
3:4
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B
1:3
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C
4:3
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D
1:4
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Solution

The correct option is A 3:4
Given: The points A(8,2) and B(6,9).
Let P(2,5) divides the line joining the give points in ratio k:1=m:n.
By section formula,
(x,y)=(mx2+nx1m+n,my2+ny1m+n)

We have,
(2,5)=(6k+8k+1,9k+2k+1)

Equating the x coordinates,
6k+8k+1=2

6k+8=2k+2

8k=6k=34

The ratio =3:4=k:1

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