To determine which explanation for the congruency of the trapezoids is correct, you need to analyze the transformations mentioned in each option:
A. Reflection over the line y = x: This transformation produces a mirror image of the shape across the line y = x. The trapezoids would be congruent as this is an isometric transformation.
B. Translation left 4 units and up 2 units: This transformation shifts the entire shape without altering its size or angles, so the trapezoids would be congruent.
C. Rotation 270° (counterclockwise): This transformation rotates the shape around a point, and while it changes the orientation, the size and shape remain the same. Thus, the trapezoids would be congruent.
D. Rotation 90° (counterclockwise): Similar to option C, this rotation also alters the orientation of the trapezoid, but it retains congruency since it does not change size or shape.
All the options, A, B, C, and D, describe isometric transformations and thus imply the trapezoids are congruent. However, without specific details about the trapezoids mentioned or their relative positions before the transformation, it would be difficult to declare which specific transformation (if applicable) demonstrates congruency in your case.
If you have more information or specific coordinates, it could clarify which transformation is indeed responsible for creating congruent trapezoids from ABCD.