Question

If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = $\frac{3}{7}$ AB and P lies on the line segment AB.

Answer 1

The coordinates of point A and B are (-2,-2) and (2,-4) respectively. since AP=$\frac{3}{7}AB$
Therefore, AP: PB=3:4
Point P divides the line segment AB in the ratio 3:4
Coordinates of P = $(\frac{3\times2+4\times(-2)}{3+4},\frac{3\times(-4)+4\times(-2)}{3+4})$
=$(\frac{6-8}{7},\frac{-12-8}{7})$
=$(-\frac{2}{7},-\frac{20}{7})$