Question

a. the transformation preserves angle measures. b. the transformation is a reflection over line y = x. c. the transformation is a translation 5 units right and 3 units down. d. the transformation is a rotation 180° clockwise about the origin. e. the transformation preserves orientation (direction).

Explanation:

Step1: Recall properties of transformations

Rigid - transformations (translations, rotations, reflections) preserve angle measures.

Step2: Analyze orientation change

A reflection changes orientation. A 180 - degree rotation changes orientation. A translation preserves orientation.

Step3: Check each option

• Option A: Rigid - transformations like the one shown preserve angle measures.
• Option B: The transformation is not a reflection over \(y = x\) as the orientation and point - mapping do not match the rule of \(y=x\) reflection (\((x,y)\to(y,x)\)).
• Option C: The transformation is not a translation 5 units right and 3 units down as the relative position of the figure with respect to the axes does not match this translation rule.
• Option D: A 180 - degree clockwise rotation about the origin changes orientation, and the given transformation does not seem to be a 180 - degree rotation about the origin.
• Option E: As mentioned, reflections and 180 - degree rotations change orientation, and this transformation does not preserve orientation in the sense described for this option.

Answer:

A. The transformation preserves angle measures.