Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?

The coordinates would be (-3.2, 6.2).

We start out finding the slope of the line segment.  Slope is rise/run:

(20-5)/(6--4) = 15/10 = 3/2

The ratio 2:3 splits the segment into 5 sections.  We will add 2/5 of the rise to the y-coordinate and 2/5 of the run to the x-coordinate:

-4+(2/5)(2)= -4+4/5 = -4+0.8= -3.2
5+(2/5)(3) = 5+6/5 = 5+1.2 = 6.2

The coordinates of P would be (-3.2, 6.2).