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Answer in Brief

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.

If *A* and *B* are two points having coordinates (−2, −2) and (2, −4) respectively, find the coordinates of *P* such that *AP* = \[\frac{3}{7}\] *AB.*

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#### Solution

Here, P(x,y) divides line segment AB, such that

`AP=3/7AB`

`"AP"/"AB"=3/7`

`rArr"AP"/("AP"+"PB")=3/7`

`rArr7AP=3AP+3PB`

`rArr4AP=3PB`

`rArr"AP"/"PB"=3/4`

P divides AB in the ratio 3:4

`x=(3xx2+4(-2))/(3+4); y=(3xx(-4)+4(-2))/(3+4)`

`x=(6-8)/7; y=(-12-8)/7`

`x=-2/7; y=-20/7`

The co ordinates of P are (-2/7,-20/7)

Concept: Division of a Line Segment

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