Question

does the transformation appear to be a rigid motion? explain. choose the correct answer below. a. the transformation is not a rigid motion because all corresponding angles and sides appear to be the same size. b. the transformation is not a rigid motion because the image appears to have a different orientation than the preimage. c. the transformation is not a rigid motion because the image and preimage do not overlap. d. the transformation is a rigid motion because all corresponding angles and sides appear to be the same size.

Explanation:

A rigid motion (isometry) preserves the size and shape of the figure. This means that all corresponding angles and sides of the pre - image and image are congruent.

• Option A: If all corresponding angles and sides are the same size, it should be a rigid motion. So, this option is incorrect.
• Option B: Orientation change does not affect whether a transformation is a rigid motion. Rotation (a type of rigid motion) changes orientation. So, this option is incorrect.
• Option C: Non - overlapping does not mean non - congruent. Translation (a type of rigid motion) can result in non - overlapping figures. So, this option is incorrect.
• Option D: Since a rigid motion preserves the size (corresponding angles and sides are congruent), if all corresponding angles and sides appear to be the same size, the transformation is a rigid motion.

Answer:

D. The transformation is a rigid motion because all corresponding angles and sides appear to be the same size.