Ratio of Directed Line Segments

Question

what are the coordinates of the point on the directed line segments from (-10, 4) to (-5,-6) that partitions the segment into a ratio of 1 to 4

Answer 1

There is a formula; it is an application of the so-called side-splitter theorem of plane geometry.

If the co-ordinates of the endpoints of a line segment are A(a,b) and C(c,d) and you want to go 100p% of the way from A toward C, the co-ordinates of that point will b

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

In your case p=.2

Have at it!