Find the coordinates of point P along the directed line segment AB, from A(-3,2) to B(5,-4) so that the ratio of AP to PB is 2 to 6.

Question

The coordinates are P(__,__)

Answer 1

Since the ratio is 2 to 6, we are dividing AB into 8 equal segments (2+6 = 8)

Between A and B, x increases by 8 and y decreases by 6

Let P = (x, y)

Then x = (x coordinate of A) + (2/8)(change in x from A to B) = -3 + (1/4)(8) = -1

y = (y coordinate of A) + (2/8)(change in y from A to B) = 2 + (1/4)(-6) = 0.5

P = (-1, 0.5)