Question

# What is the ratio in which P(2,5) divides the line joining the points (8,2) and (âˆ’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 3:4Given: 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=−6⇒k=34∴ The ratio =3:4=k:1

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