Question

A rotation is an isometry?

a) Yes, a rotation is an isometry.
b) No, a rotation is a transformation that changes the shape and size of a figure.
c) A rotation can be an isometry depending on the specific angles involved.
d) A rotation is an algebraic equation, not an isometry.

Answer 1

A rotation is an isometry as it is a transformation that preserves distances and angles, maintaining the size and shape of the figure unchanged.

Step-by-step explanation:

Yes, a rotation is an isometry. An isometry is a transformation that preserves distances and angles, meaning that the size and shape of the figure are unchanged. Rotations, specifically, are a type of isometric transformation where a figure is turned around a fixed point, known as the center of rotation, by a certain angle. This action keeps the distance between points constant, thus maintaining the figure's shape and size. In the context provided, whether we consider the cube's C4 axes or C3 axes, the cube's structure remains unchanged with its spatial properties intact, signifying that a rotation is indeed an isometry.