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).