Directed Line Segments 2

Question

Given A(-6,-4) and B(0,8) on directed line segment AB, find point P on the segment such that AP = 3PB.

Answer 1

If AP = 3PB, then AP is 3/4 of the way from A(-6,-4) to B(0,8)

x coordinate of P is -6 + 3/4(0--6) = -6 + 3/4(6) = -6 + 9/2 = -1.5

y coordinate of P is -4 + 3/4(8--4) = -4 + 3/4 (12) = -4 + 9 = 5

P is (-1.5,5)