Thread: [SOLVED] Proof regarding reflections/rotations

Prove that if point is on line , and is any angle, then both and are both reflections. What are their axes?

Originally Posted by Pinkk

Prove that if point is on line , and is any angle, then both and 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

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...

Any ideas?

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