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Find the co-ordinates of a point P on th...

Find the co-ordinates of a point P on the line segment joining `A(1,2)and B(6,7)` such that `AP=2/5AB.`

A

`(3,4)`

B

`(5,4)`

C

`(7,4)`

D

`(3,5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`AP = (2)/(5)AB rArr (AP)/(AB) = (2)/(5)`
` rArr (AP)/(AP + PB) = (2)/(5) rArr 5AP= 2AP +2PB`
`rArr 3AP = 2PB rArr (AP)/(PB) = (2)/(3) rArr AP:PB = 2:3.`
So, P divides AB in the ratio 2 :3.
`therefore `coordinates of P are `((2 xx 6 +3 xx 1)/(2+3), (2 xx 7 + 3 xx 2)/(2+3)) = ((15)/(5), (20)/(5)) = (3, 4).`
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