This is the problem:

I have a line L defined by (X1,Y1) – (X2,Y2) and a pointP (Xp, Yp) on L that I want to move a scalar distance D along that line and get point Q (Xq, Yq)

This is the question:

Is there a fast (no sqrt, preferably integer) algorithm to calculate Q? Is there some integer arithmetic that draws upon something like the error function used in line drawing algorithms?

This is a c# (preferably) coding question.

This is what I have tried:
I can get the unit vector of the line with a sqrt function, but I have many lines and hope for a faster algo