Question

a. describe a sequence of rigid motions for each piano that maps the piano from its current location to the new location
b. describe a single rotation for each piano that maps the piano from its current location to the new location (hint you can find two reflections to determine the center of rotation.)
b. find a single rotation for piano 1 choose the correct answer below
a. rotate ( 90^{circ} ) counterclockwise about the point 2 units rights and 4 units down from point a
b. rotate ( 90^{circ} ) counterclockwise about the point 2 units right and 2 units down from point a
c. rotate ( 90^{circ} ) counterclockwise about the point 2 units down from point a
d. rotate ( 90^{circ} ) counterclockwise about the point 1 unit right and 3 units down from point a

Explanation:

Step1: Analyze the motion of Piano 1

We need to find a single rotation. By observing the transformation from the current location to the new location of Piano 1, we consider the properties of rotation.

Step2: Check each option

• Option A: Rotate \(90^{\circ}\) counter - clockwise about the point 2 units right and 4 units down from point A. This does not match the required transformation.
• Option B: Rotate \(90^{\circ}\) counter - clockwise about the point 2 units right and 2 units down from point A. This does not match the required transformation.
• Option C: Rotate \(90^{\circ}\) counter - clockwise about the point 2 units down from point A. This matches the transformation of Piano 1.
• Option D: Rotate \(90^{\circ}\) counter - clockwise about the point 1 unit right and 3 units down from point A. This does not match the required transformation.

Answer:

C. Rotate \(90^{\circ}\) counterclockwise about the point 2 units down from point A.