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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

User Amarildo
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1 Answer

3 votes

Final answer:

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.

User Masta
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8.2k points
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