How to find a point on a line at a given distance from a given point on the same line (given the equation of the line)? You are given a point P(x,y) on a line of equation ax + by + c = 0. I want another point, Q(a,b) on the same line which is at a distance d from P. There will be two points. I want to find both and know which side of P each one lies.
There are related questions in this forum, but I didn't get what I am exactly looking for. Sorry for beating around the bush, and thanks for any help... Please give me an elaborate explanation. Thanks once again!!!

The direction of the given line is $$\binom {-b}a$$
So the two points you are looking for have position vectors $$\binom xy\pm\frac{d}{\sqrt{a^2+b^2}}\binom {-b}a$$
