The endpoints of the directed line segment AB are A(-9,4) and B(7,-1). FIND THE COORDINATES OF POINT P ALONG AB SO THE RATIO OF AP TO PB IS 3 TO 1

Answer 1

If the end points are A(a,b) and C(c,d) and you want the point 3/4 of the way from A to C

the co-ordinates are (.25a+.75c, .25b+.75d).

This is an application of the side-splitter theorem from plane geometry and it would certainly be worth your time to go show your self that proof. And if you can't prove it, make a comment to that effect and I will try to show you how to do it.