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Math Help - [SOLVED] Proof regarding reflections/rotations

  1. #1
    Senior Member Pinkk's Avatar
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    [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?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Pinkk View Post
    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
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  3. #3
    Senior Member Pinkk's Avatar
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    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...
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  4. #4
    Senior Member Pinkk's Avatar
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    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.
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