with an extra reflection on the first one you get the second one.
So one is preserving orientation but the other is not.
"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 so and "
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!