# Thread: [SOLVED] Proof regarding reflections/rotations

1. ## [SOLVED] Proof regarding reflections/rotations

Prove that if point $P$ is on line $m$, and $\theta$ is any angle, then both $R_{P,\theta} \circ \rho_{m}$ and $\rho_{m} \circ R_{P,\theta}$ are both reflections. What are their axes?

2. Originally Posted by Pinkk
Prove that if point $P$ is on line $m$, and $\theta$ is any angle, then both $R_{P,\theta} \circ \rho_{m}$ and $\rho_{m} \circ R_{P,\theta}$ are both reflections. What are their axes?
Would you mind defining some of the terms for us? Like your last problem...sometimes people have different notations

3. A rotation of angle theta around any point C is a function that maps point P to point P' such that CP = CP' and angle PCP' is theta (counterclockwise).

A reflection is the transformation that fixes every point on the line of reflection and associates to each point P not on that line a unique point P' such that the line of reflection is the perpendicular bisector of the line segment PP'.

I started working on this proof thinking that the point being rotated/reflected was on the given line m, but that doesn't have to be the case...

4. Any ideas?

Edit: Nevermind, just figured out to construct a line n that meets line m at point P at an angle of $\frac{\theta}{2}$ so I could break down the rotation into two reflections, and getting the reflections about line m to cancel each other out.