>Thanks for your help. i
>can't really answer your question,
>why i'd want to, i
>guess it's just for completeness.
> it annoys me when
>i don't know how to
>do something that interests me.

What I asked was, "What is it you see in your mind's eye when you talk about those reflections?" The reason I asked was because there may be several kinds of reflections - that's all.

>my problem now is how to find
>the equation of the new
>line. i realise this
>is probably a bit too
>much to go into easily,
>but do you know where
>i can find it out?
>

It's pure analytic geometry and/or some Calculus. The most essential part of you query is being able to find the point on a given curve nearest to a given point.

Say, you are given a point (x0, y0) whose reflection in y = x2 you intend to find. You'll have to minimize the sqaure of the distance:

d(x) = (x - x0)2 + (x2 - y0)2

Equate the derivative to 0 and see if you can solve the equation. If you can, assume x1 is a solution. Then the reflection point is given by

(x, y) = 2(x1, y1) - (x0, y0)