Question

under a transformation, a preimage and its image are both squares with side length 3. the image, however, is rotated with respect to the preimage. is the transformation a rigid motion? explain.
a rigid motion is a transformation that preserves
each side in the preimage has length and each side in the image has length, so the transformation length. each angle in the preimage has a measure of and each angle in the image has a measure of, so the transformation angle measure. therefore, the transformation a rigid motion.
(do not include the degree symbol in your answers.)

Explanation:

Step1: Recall the properties of rigid motion

A rigid motion preserves distance (length) and angle measure.

Step2: Analyze the side - length

Each side in the pre - image has length \(3\) and each side in the image has length \(3\), so the transformation preserves length.

Step3: Analyze the angle measure

Each angle in the pre - image has a measure of \(90\) (since it's a square) and each angle in the image has a measure of \(90\) (still a square), so the transformation preserves angle measure.

Answer:

A rigid motion is a transformation that preserves distance (length) and angle measure. Each side in the preimage has length \(3\) and each side in the image has length \(3\), so the transformation preserves length. Each angle in the preimage has a measure of \(90\) and each angle in the image has a measure of \(90\), so the transformation preserves angle measure. Therefore, the transformation is a rigid motion.