To determine which sequence of transformations maps a quadrilateral onto itself, we need to analyze each option to see if the transformations result in the same quadrilateral.
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Step 1: Reflect across x-axis; Step 2: Reflect across y-axis.
- Reflecting across the x-axis flips the quadrilateral over the x-axis.
- Reflecting that result over the y-axis flips it back over the y-axis.
- The combined effect of these two transformations will result in moving each point from (x, y) to (-x, -y), effectively returning the quadrilateral to its original position. So, this sequence does map the quadrilateral onto itself.
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Step 1: Reflect across y-axis; Step 2: Reflect across the line y=-1.
- Reflecting across the y-axis flips the quadrilateral over the y-axis.
- Reflecting that result across the line y=-1 does not change the original position symmetry. However, it will generally change the position of the quadrilateral unless it lies symmetrically about that line.
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Step 1: Reflect across the line y=x; Step 2: Reflect across the line y=-x.
- Reflecting across y=x swaps the x and y coordinates of all points.
- Reflecting that result across y=-x reverses the direction in a way that does not place the quadrilateral back onto its original position.
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Step 1: Reflect across x-axis; Step 2: Reflect across the line x=-1.
- Reflecting across the x-axis flips the quadrilateral over the x-axis.
- Reflecting across the line x=-1 shifts the quadrilateral horizontally. So the configuration will change, and it will not map onto itself.
After analyzing all these options, the first sequence is the only one that maps the quadrilateral onto itself.
The correct answer: Step 1: Reflect across x-axis; Step 2: Reflect across y-axis.
1 answer