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