To determine which explanation for the congruency of the trapezoids is correct, we need to consider the transformations described:
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Reflection over the line y = x: This transformation would swap the x and y coordinates of the vertices of trapezoid ABCD. If trapezoid ABCD and its reflected version are congruent, this transformation would result in congruent trapezoids.
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Rotation 270° (counterclockwise): A 270° rotation (or -90° rotation) would change the position of the trapezoid in a specific way, but it would maintain congruency since rotations preserve shape and size.
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Rotation 90° (counterclockwise): A 90° counterclockwise rotation would also change the position of the trapezoid but would keep it congruent for the same reasons as above.
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Translation left 4 units and up 2 units: Translation moves the entire shape without altering its dimensions, thus preserving congruency.
Given these transformations maintain congruency, the explanation that correctly identifies how trapezoids ABCD are congruent depends on the context. Since all transformations listed preserve congruence, any of them could potentially be correct as long as they describe a transformation that was actually applied to trapezoid ABCD.
However, without additional context or information about the trapezoids' initial and final positions, it isn't possible to determine definitively which specific explanation is the "correct" one. If you know the specific transformation that was applied to obtain the congruent trapezoid, that would determine the correct explanation.
2 answers