Note that it is impossible to express the line x=0 this way.

More general way to express a line through the origin is ax + by = 0.

Alternatively we can use an angle, say .

Probably easiest is to think in terms of vectors. Let O be the origin, let L be a line through O, let P be a point, and let P' be the reflection of P across L. Note that P and P' have the same distance from the origin (same magnitude), and note that connecting O, P, and P' either gives you a line segment or an isosceles triangle..

Edit: You might find this useful, particularly the intro

http://planetmath.org/encyclopedia/D...ionMatrix.html