1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Geometry Topology Isometry Date
Projective Plane Proof Jan 30, 2018
Find intersections between sphere and parallel tangent planes Jan 9, 2018
Parametrize the Curve of Intersection Oct 14, 2017
Asymptotic geometry question Sep 29, 2017
Spivak & Dimension of Manifold Jan 10, 2016