Question

why are translations, reflections, and rotations rigid transformations?

Explanation:

A rigid transformation (also called an isometry) is a transformation that preserves the shape and size of a figure. Translations slide a figure without changing its shape, size, or orientation. Reflections flip a figure over a line (the line of reflection), and the distance between any two points on the original figure and their images remains the same, so the shape and size are preserved. Rotations turn a figure around a fixed point (the center of rotation), and again, the distances between points (and thus the shape and size of the figure) are unchanged. In all three transformations, the pre - image and the image are congruent (same shape and size), which is the defining characteristic of a rigid transformation.

Answer:

Translations, reflections, and rotations are rigid transformations because they preserve the shape and size of a figure (i.e., the pre - image and image are congruent). Translations slide the figure without altering its shape, size, or orientation. Reflections flip the figure over a line, and the distances between points in the pre - image and their corresponding points in the image remain equal. Rotations turn the figure around a fixed point, and the distances between points (and thus the overall shape and size of the figure) are unchanged.