Find the point p along the directed line segment from point a(-16,-8) to point b(0,-17) that divides the segment in the ratio 7 to 6

P(-7.38,-12.85)

Steps:

Draw the directed line in a chart, including points A and B.

Look for the x coordinate of P:

the distance |B-A| along the x coord is |0-(-16)|=16

we are looking for a proportion of 7/13 of that:

the x coord of P is 16*7/13 to the right of -16, or -16+8.62= -7.38

Look for  y coordinate of P:

the distance |B-A| along the y coord is |-17-(-8)|=9

we are looking for a proportion of 7/13 of that:

the y coord of P is 9*7/13 down from -8, or -8-4.85= -12.85

so the point P is P(-7.38,12.85)