Question

determine whether the pair of objects is congruent. if so, describe a composition of rigid motions that maps one object onto the other.

choose the correct answer below.

a. the objects are congruent. to map the object on the left to the object on the right, rotate it 180° around its center and reflect over a vertical line.
b. the objects are congruent. to map the object on the left to the object on the right, translate the left object right, rotate it 270° counterclockwise around its center, and reflect it across a vertical line.
c. the objects are congruent. to map the object on the left to the object on the right, translate the left object down and reflect it across a vertical line.
d. the objects are not congruent.

Explanation:

• Rigid motions (translation, rotation, reflection) preserve congruence.
• Analyze each option:
• Option A: Rotating \(180^{\circ}\) and reflecting over a vertical line can map one object to the other as rigid motions.
• Option B: \(270^{\circ}\) counter - clockwise rotation is not needed as \(180^{\circ}\) rotation suffices.
• Option C: Translating down is incorrect as the main transformation is rotation and reflection.
• Option D: Incorrect as objects are congruent.

Answer:

A. The objects are congruent. To map the object on the left to the object on the right, rotate it \(180^{\circ}\) around its center and reflect over a vertical line.