Proofs of the Reflection Rules I couldn't find a formal proof for the rule:
when a point $(a,b)$ is reflected along $y=x$, it becomes $(b,a)$.
I tried to prove it by sketching out the situation:

However, I still don't know how to prove that $b'=b, a'=a$.
Furthermore, I just want to make sure, for the following two rules:

*

*Reflection Across Y-Axis. $(x,y)\to(-x,y)$

*Reflection Across X-Axis. $(x,y)\to(x,-y)$.

Do they have formal proofs or do we just prove them by visualizing where a point ends up to be on a cartesian plane?

Triangles $(0,0)(1,1)(a,b)$ and $(0,0)(1,1)(b,a)$ are congruent because corresponding sides have equal length (by Pythagoras).
