What are the coordinates of the point on the directed line segment from (-1, -8) to (5, -2)that partitions the segment into a ratio of 1 to 2?

Answer 1

If the point (x,y) divides the line segment into two parts that are a ratio of 1:2, then (x,y) is 1/3 of the distance from (-1,-8) to (5,-2).

Determine 1/3 of the x distance from 5 to -1: (5--1)/3 = 2 and add it to -1 --> 1

Determine 1/3 of the y distance from 2 to -8: (2--8)/3 = 2 and add it to -8 --> -6

Point (x,y) is (1,-6)

Answer 2

Let this point is(a, b). Then <a + 1, b + 8> = 1/3<6, 6> = <2, 2>; a + 1 = 2; a = 1; b + 8 = 2; b = - 6.

Point (1, - 6) devide this segment in 1 to 2 ratio.