Question

What are the coordinates of the point on the directed line segment from (4, -3)(4,−3) to (9, -8)(9,−8) that partitions the segment into a ratio of 3 to 2?

Answer 1

(7, -6)

Explanation:

You want to find point X on the segment from A to B such that ...

(X -A)/(B -X) = 3/2

2(X -A) = 3(B -X) . . . . . . cross multiply

2X -2A = 3B -3X . . . . . eliminate parentheses

5X = 2A +3B . . . . . . . . add 3X +2A

X = (2A +3B)/5 . . . . . . . divide by 5

Filling in the given points for A and B, we have ...

X = (2(4, -3) +3(9, -8))/5 = (8+27, -6-24)/5 = (35, -30)/5

X = (7, -6)

The point that divides the segment in the proportions 3:2 is (7, -6).