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)