What are the coordinates of the point on the directed line segment from (−8,−3) to 7,9) that partitions the segment into a ratio of 2 to 1?

Answer 1

Let A = (-8, -3), B = (7, 9), and let P = (x,y) be the point on line segment AB that divides AB in the ratio 2:1.

Partitioning the segment in the ratio 2:1 means that we are dividing AB into three congruent segments. P is 2/3 of the way from A to B. As we move along AB from A to B, the x-coordinates increase by 15 and the y-coordinates increase by 12.

x = -8 + (2/3)(15) = 2 and y = -3 + (2/3)(12) = 5

So, P = (2, 5)