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

Answer 1

A = (4,-3)

C= (9,-8)

Length AC = √(9-4)²+(-8+3)² = 5√2 Let B be the point between A and C

3:2 = 3/5 : 2/5

(3/5)(5√2) = 3√2 = √(3²+3²) = √((x-4)²+(y+3)²)

(2/5)(5√2) = 2√2 = √(2²+2²) = √(9-x)²+(-8-y)²)

x-4 = 3 --> x = 7

y+3 = -3 --> y = -6

or

9-x = 2 --> x=7

-8-y = -2 --> y = -6

B = (7,-6)

Answer 2

The x coordinate is 3/5 the way from 4 to 9

The y coordinate is 3/5 the way from -3 to -8