P is a point on the line joining A (4, 3) and B (-2, 6) such that 5AP = 2BP. Find the co-ordinates of P.

Given,

⇒ 5AP = 2BP

⇒ $\dfrac{AP}{BP} = \dfrac{2}{5}$

⇒ AP : PB = 2 : 5.

Let co-ordinates of P be (x, y).

By formula,

$x = \dfrac{m$1x2 + m2x1}{m1 + m2} \\[1em] = \dfrac{2 \times -2 + 5 \times 4}{2 + 5} \\[1em] = \dfrac{-4 + 20}{7} \\[1em] = \dfrac{16}{7} \\[1em] y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] = \dfrac{2 \times 6 + 5 \times 3}{2 + 5} \\[1em] = \dfrac{12 + 15}{7} \\[1em] = \dfrac{27}{7}.

Hence, co-ordinates of P = $\Big(\dfrac{16}{7}, \dfrac{27}{7}\Big).$