coordinate of shorter line

Question

If I have a line segment with endpoints AB,CD. The length of the line is 5 units.

If I make the line shorter (eg. 3 units), and one of the endpoints is still AB, how do I figure out what the new CD is?

Thanks for the help

Answer 1

We assume that your A, B, C, D are coordinates.

So we will more conventionally call them $(a,b)$ and $(c,d)$.

For your particular case, the coordinates of the new endpoint are $(x,y)$, where $$x=a+\frac{3}{5}(c-a)\qquad\text{and} \qquad y=b+\frac{3}{5}(d-b).$$