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

Explanation:

Step1: Understand the concept of rigid motion

A rigid motion (also called an isometry) is a transformation that preserves the size and shape of a figure. That means all corresponding angles and sides of the pre - image and image are congruent.

Step2: Analyze each option

• Option A: Orientation change does not prevent a transformation from being a rigid motion. Rotation (a type of rigid motion) changes the orientation.
• Option B: Non - overlapping does not mean it is not a rigid motion. Translations (a type of rigid motion) result in non - overlapping pre - image and image.
• Option C: If all corresponding angles and sides appear to be the same size, then by the definition of rigid motion (preserving size and shape), the transformation is a rigid motion.
• Option D: If all corresponding angles and sides are the same size, it should be a rigid motion, not “not a rigid motion”.

Answer:

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