To determine the correct sequence of rigid transformations performed on figure ABCD to produce figure WXYZ, we need to analyze the transformations described in the responses:
- Shifting: Moving a figure left, right, up, or down without changing its orientation.
- Rotation: Turning a figure around a fixed point (usually the origin) by a specific angle.
The options provided suggest two transformations: a combination of shifting and rotation.
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Shift 3 units left and 5 units up: This means if point A had coordinates (x, y), after the transformation, it would be at (x - 3, y + 5).
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Rotation of 90° counterclockwise: This transformation changes the coordinates (x, y) to (-y, x).
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Rotation of -270° (clockwise): This is equivalent to a rotation of 90° counterclockwise as rotating −270° around a point has the same effect as rotating 90° counterclockwise.
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Rotation of 90° clockwise: Changes (x, y) to (y, -x).
In this scenario, we want to verify the transformations:
- Shifting: We would first need to check if shifting ABCD left and up will get it closer to the position of WXYZ.
- Rotation: Then, we need to determine if a rotation would align the newly shifted ABCD to overlap WXYZ perfectly.
Based on typical coordinates and transformations to get from one shape to another, the most logical transformation that matches the options provided is:
- ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
This transformation would change the location of ABCD appropriately, and the rotation would place it in the correct orientation to match WXYZ.
Thus, the correct answer is: ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
1 answer