Question

What are the coordinates of the point on the directed line segment from (-8,2) to (7,-3) that partitions the segment into a ratio of 3 to 2?

Answer 1

(1, -1)

Explanation:

One way to find the point is this.

The point P that divides AB into segments AP/PB = 3/2 can be found to be ...

P = A +(AP/AB)(B -A)

P = (-8, 2) + (3/5)(7-(-8), -3-2)

P = (-8, 2) +3/5(15, -5) = (-8, 2) +(9, -3) = (-8+9, 2-3)

P = (1, -1)

__

Another way to find the point is ...

AP/PB = 3/2

2(P -A) = 3(B -P)

5P = 3B +2A

P = (3B +2A)/5 = (3(7, -3) +2(-8, 2))/5 = (21 -16, -9 +4)/5 = (5, -5)/5

P = (1, -1)