Question

what are the coordinates of the point on the directed line segment from (-1, -10) to (7,6) that partitions the segment into a ratio of 1 to 3

Answer 1

The point will be 1/4 of the distance along the line hence cutting it into 1/4 : 3/4
-1 + (7 - -1)/4 = -1 + 2 = 1
-10 + (6 - -10)/4 = -10 + 4 = -6
The point is at (1 , -6)