Question

What set of reflections and rotations would carry rectangle ABCD onto itself?

a) Reflect over the y-axis, reflect over the x-axis, rotate 180°
b) Rotate 180°, reflect over the x-axis, reflect over the line y=x
c) Reflect over the x-axis, rotate 180°, reflect over the x-axis
d) Rotate 180°, reflect over the y-axis, reflect over the line y=x

Answer 1

The correct set of reflections and rotations that would carry rectangle ABCD onto itself is option d) Rotate 180°, reflect over the y-axis, reflect over the line y=x.

Step-by-step explanation:

The correct set of reflections and rotations that would carry rectangle ABCD onto itself is option d) Rotate 180°, reflect over the y-axis, reflect over the line y=x.

To carry rectangle ABCD onto itself, we need to perform a rotation of 180° (half a full rotation) followed by two reflections. First, we reflect over the y-axis to maintain the same x-coordinates but reverse the y-coordinates. Then, we reflect over the line y=x to swap the x-coordinates with the y-coordinates.

By performing these transformations in the given order, we can ensure that the rectangle remains the same shape and orientation.