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 $\displaystyle \phi $ so $\displaystyle \phi(P) = P' $ and $\displaystyle \phi(Q) = Q' $"

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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!