Geometry distance

Question

Find the coordinates of the point that divides the directed line segment MN with the coordinates of endpoints at M(-4,0) and M(0,4) in the ratio 3:1?

Answer 1

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

If the endpoints of a segment are A(a,b) and C(c,d) and you want 100p% of the way from A to B,

the co-ordinates will be [pc+(1-p)a,pd+(1-p)d].

In your case p=.75.