Help with geometry homework

Question

segment AB has endpoints A(-7,2) and B(9,-6) point P lies on AB such that AP:BP = 3:1. determine the coordinates of P.

B) a dilation of P centered at A maps P into B. what dilation constant is needed?

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Answer 1

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

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

In your case p=.75 (3/4 of the way from A to B)

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

I will leave the dilation problem to you.