Question

movers need to move the pianos shown in the diagram.
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.)
find a single rotation for piano 2 choose the correct answer below.
o a. rotate 180° about the point 8 units left and 2 units down from point j
o b. rotate 180° about the point 8 units left from point j
o c. rotate 180° about the point 8 units left and 4 units down from point j
o d. rotate 180° about the point 8 units left and 2 units up from point j

Explanation:

Step1: Analyze each option

• Option A: Rotate \(180^{\circ}\) about the point \(8\) units left and \(2\) units down from point \(J\).
• Option B: Rotate \(180^{\circ}\) about the point \(8\) units left from point \(J\).
• Option C: Rotate \(180^{\circ}\) about the point \(8\) units left and \(4\) units down from point \(J\).
• Option D: Rotate \(180^{\circ}\) about the point \(8\) units left and \(2\) units up from point \(J\).

Step2: Determine the correct rotation center

By visual inspection or using the properties of rotation (a \(180^{\circ}\) rotation about a point maps a figure to its opposite position), we find that the correct rotation is a \(180^{\circ}\) rotation about the point \(8\) units left and \(2\) units down from point \(J\).

Answer:

A. Rotate \(180^{\circ}\) about the point \(8\) units left and \(2\) units down from point \(J\)