What set of reflections and rotations would carry rectangle ABCD onto itself?Group of answer choicesRotate 180°, reflect over the y-axis, reflect over the line y = xReflect over the x-axis, rotate 180°, reflect over the x-axisRotate 180°, reflect over the x-axis, reflect over the line y = xReflect over the y-axis, reflect over the x-axis, rotate 180°
Question
What set of reflections and rotations would carry rectangle ABCD onto itself?Group of answer choicesRotate 180°, reflect over the y-axis, reflect over the line y = xReflect over the x-axis, rotate 180°, reflect over the x-axisRotate 180°, reflect over the x-axis, reflect over the line y = xReflect over the y-axis, reflect over the x-axis, rotate 180°
Solution
The set of reflections and rotations that would carry rectangle ABCD onto itself is: Rotate 180°, reflect over the x-axis, reflect over the line y = x.
Here's why:
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Rotate 180°: This will flip the rectangle around, but it will still look the same because all sides and angles in a rectangle are equal.
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Reflect over the x-axis: This will flip the rectangle upside down. Again, because all sides and angles in a rectangle are equal, it will still look the same.
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Reflect over the line y = x: This will flip the rectangle diagonally. Because all sides and angles in a rectangle are equal, it will still look the same.
So, after these three transformations, the rectangle ABCD will have been carried onto itself.
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