Question

If P is a point on the segment joining X(-2,-2) and Y(8,3), find the coordinates of point P if XP:PY = 2:3.

Answer 1

make a sketch and set up simple ratios

let the point P be P(x,y)
(8-x)/(x+2) = 3/2
3x + 6 = 16 - 2x
5x = 10
x = 2

(3-y)/(y+2) = 3/2
3y + 6 = 6 - 2y
5y = 0
y = 0

P is (2,0)

verify with your sketch