Question

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

Answer 1

Given that AP = 3/7 AB

⇒ 7AP = 3AB

⇒ 7AP = 3(AP + BP)

⇒ 7AP = 3AP + 3BP

⇒ 7AP - 3AP = 3PB

⇒ 4AP = 3PB

⇒ \(\frac{AP}{PB}=\frac34\)

Hence, P dividences AB in the ratio 3: 4

By section formula, the coordinates of point P are

(x, y) = \(\left(\frac{3\times2+4\times-2}{3+4},\frac{3\times-4+4\times-2}{3+4}\right)\)

\(=(\frac{6-8}7,\frac{-12-8}7)\)

\(=(\frac{-2}7,\frac{-20}7)\)