To determine which explanation for the congruency of the trapezoids is correct, we need to analyze the transformations mentioned.
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Rotation 90° counterclockwise: This transformation would result in a new shape that may not be congruent, depending on the trapezoid's orientation.
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Translation left 4 units and up 2 units: Translation does not change the shape or size, so if both trapezoids have the same dimensions and shape, they would be congruent after this transformation.
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Rotation 270° counterclockwise: This is equivalent to a 90° clockwise rotation. Similar to the 90° counterclockwise rotation, it may not maintain congruency depending on the orientation.
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Reflection over the line y=x: This transformation mirrors the trapezoid, which also retains congruency if the trapezoids are identical in shape and size.
Based on these analyses, the most straightforward explanation that ensures congruency without altering dimensions would be:
The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
This explanation straightforwardly maintains the dimensions without any potential changes in orientation or reflection.