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

Explanation:

Step1: Recall the definition of rigid motion

Rigid motion (isometry) preserves distances (side - lengths) and angles.

Step2: Analyze each option

• Option A:

If the corresponding sides are not the same size, then the transformation does not preserve distances. Since rigid motion requires distance preservation, this option is correct.

• Option B:

If the sides were the same size (by visual inspection, they are not), but since they are not, this option is wrong.

• Option C:

Orientation is not the key factor for rigid motion. Rigid motion is about distance and angle preservation. Even if the orientation is the same, if distances are not preserved (as in this case), it is not a rigid motion. So this option is wrong.

• Option D:

Just having the same - sized angles is not sufficient. Rigid motion also requires side - length (distance) preservation. So this option is wrong.

Answer:

A. The transformation is not a rigid motion because the corresponding sides do not appear to be the same size.