To determine which sequence of rigid transformations resulted in figure WXYZ being congruent to figure ABCD, we need to break down the options provided:
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ABCD was first shifted 3 units to the left and 5 units up, then rotated 90° (counterclockwise).
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ABCD was first rotated -270° (clockwise), then shifted 3 units to the left and 5 units up.
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ABCD was first shifted 3 units to the left and 5 units up, then rotated -90° (clockwise).
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ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up.
To determine which transformation corresponds to the movement to produce WXYZ, we need to analyze the results of each transformation.
- Shifting 3 units left and 5 units up modifies the position of the figure in a straightforward way.
- Rotating the figure (either clockwise or counterclockwise) changes the orientation but retains congruence.
Let’s evaluate each option based on the transformations described:
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Option 1: Shifts the figure and then rotates it. The end position will be different from just a rotation alone.
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Option 2: Rotates the figure first and then shifts it, which might yield a congruent figure depending on the orientation and shift.
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Option 3: This option also combines a shift followed by a rotation, similar to option 1.
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Option 4: Rotates the figure first and then shifts it, similar to option 2.
To summarize:
- If WXYZ was created by first rotating ABCD and then shifting its position, options 2 and 4 are candidates.
- If it was created via a shift followed by a rotation, options 1 and 3 would apply.
Without specific details about the original coordinates of ABCD or the final coordinates of WXYZ, it may not be possible to definitively select one option over the other. However, for a clear and efficient transformation approach, many problems might assume options where rotation precedes translation to maintain the orientation of a figure, favoring options 2 or 4.
Thus, if your task is to merely select between coupled interpretations, I would recommend choosing Option 4: "ABCD was first rotated 90° (counterclockwise), then shifted 3 units to the left and 5 units up," since it assumes an intuitive order for congruent transformations that alters shape to follow a designated shift pathway after rotational orientation. However, more concrete spatial data would confirm this selection definitively.