Finding a point of a line that is an exact distance from a point (2D)

is the distance of X and Y provided? or a single value for the distance?
a lot of points can be produced if X and Y distances are not given

is p4 exactly in between p1 and p2?

Yes, you just need to find the intersection between the line segment, and a circle with p3 as center point and the distance as radius.

Note that there could be two intersection points.

Or to make things a bit more explicit :

A line through two points p1(x1, y1) and p2(x2, y2) has this equation :

        y = y1 + ((y2 - y1)/(x2 - x1)) * (x - x1)

A circle with p3(x3, y3) as center and radius r has this equation :

        (x - x3)² + (y - y3)² = r²

These are two equations with two unknowns (x and y), which can be solved to find two (x,y) points.

Then you simply need to check if those points are on the line segment or not.

If you need further assistance, then I'll be available again in about an hour ;)

That's the way I was heading put somehow ended up with (p2x - p1x)^2 = -(p2x - p1x)^2 which is obviously a mistake. 50 bonus points as promised for code. Thank you!