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

Answer 1

If the co-ordinates ends of a line segment are A(a,b) and C(c,d) and you want to find thes co-ordinates ofa point 100p% of the way from A to C, then the co-ordinates are

[(1-p)a+pc,(1-p)b+pd].

In your case p=.4.

BTW: This is an application of the so-called Side-splitter Theorem of plane geometry.