Reflection of (a,b) across standard lines:

• x-axis: (a, -b)
• y-axis: (-a, b)
• origin: (-a, -b)
• y = x: (b, a)
• y = -x: (-b, -a)
• x = c: (2c-a, b)
• y = c: (a, 2c-b)

Reflection across a general line Ax+By+C=0: Image of (x0,y0) is $\frac{x0 - 2A(Ax0+By0+C}{(A^2+B^2)}$, y0 - 2B$\frac{Ax0+By0+C}{(A^2+B^2)}$).

This is the same as the perpendicular-foot-image formula from 3D geometry, restricted to 2D.