MathCastle
GeometryChallengeTransformations

Transformations · Challenge problem

Consider these five compositions of two transformations of the plane: (1) a reflection, then a translation; (2) a rotation, then a dilation with scale factor 22; (3) a dilation with scale factor −1-1, then a rotation; (4) a dilation with scale factor 33, then a dilation with scale factor 13\dfrac13; (5) a reflection, then a dilation with scale factor −1-1. For how many of the five is the composition GUARANTEED to preserve every distance (be an isometry)?