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Math Help - Euclidean Isometries

  1. #1
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    Euclidean Isometries


    "
    Let P, Q, P' and Q' be 4 points in the euclidean plane where distance(P,Q) = distance(P', Q') and the distance is not 0. Show there are precisely 2 isometries \phi so \phi(P) = P' and \phi(Q) = Q' "

    I think that there's at least one such isometry because the euclidean plane is isotropic, which means that a translation/rotation exists to map these points. But I don't know how to define 2 such phis, or what the differences are between them.

    Thank you so much for any help!
    Last edited by kimberu; September 13th 2010 at 11:31 PM. Reason: bad format, sorry!
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  2. #2
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    with an extra reflection on the first one you get the second one.
    So one is preserving orientation but the other is not.
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