# 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. - Mathematics

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.

#### 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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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 9 Constructions
Exercise 6.3 | Q 39 | Page 30