Question

If O is the origin and Q(-2, -4) is a point on OP such that OQ = (1/3)OP, find the coordinates of P.

Answer 1

Let P = (x, y). See Fig.

Now OQ = (1/3)OP ⇒ OP = 3OQ

⇒OQ:QP ⇒ 1 : 2

Therefore

(-2, -4) = Q = (x/3, y/3)

⇒ x/3 = -2, y/3 = -4

⇒ x = -6, y = -12

⇒ P = (-6, -12)