Question

1. abcd is a square. given abcd ≅ abcd, describe a pair of rigid motions that maps abcd to abcd. a. translation 6 units down, translation 10 units right b. reflection across the x - axis, translation 6 units right c. translation 6 units up, translation 10 units left d. reflection across the x - axis, translation 6 units up

Explanation:

Step1: Analyze the orientation change

The square \(ABCD\) above the \(x -\)axis needs to be flipped to match the orientation of \(A'B'C'D'\) below the \(x -\)axis. A reflection across the \(x -\)axis will change the sign of the \(y -\)coordinates of all the points of the square, which is a necessary first - step for the transformation.

Step2: Analyze the vertical displacement

After reflection across the \(x -\)axis, we need to move the square vertically. By observing the position of the square after reflection and the target square \(A'B'C'D'\), we see that a translation of 6 units down is required to match their vertical positions.

Step3: Analyze the horizontal displacement

After reflection and vertical translation, we observe that a translation of 10 units right is required to match the horizontal positions of the two squares. But looking at the options, the correct sequence of rigid motions that match the transformation from \(ABCD\) to \(A'B'C'D'\) considering the orientation and position is reflection across the \(x -\)axis and then translation 6 units right.

Answer:

B. Reflection across the x - axis, translation 6 units right