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Homework Help: Geometry/Topology Isometry question

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data
    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 [tex]\varphi[/tex] so [tex]\varphi(Q) = Q^{l}[/tex] and [tex]\varphi(P) = P^{l}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    So I know (I think) that there's at least one such isometry because the plane is isotropic, which means that a translation/rotation exists to map these points. But I don't know how to define 2 such [tex]\varphi[/tex]s, or what the differences are between them.

    Thank you so much for any help!
  2. jcsd
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