Answer:
Reflection in the line y = -x.
Step-by-step explanation:
You want the transformation that maps parallelogram A to parallelogram B.
Transformation
The two parallelograms are the same size, so there is no dilation involved.
They have different orientations in that the short sides are vertical in one figure and horizontal in the other. However a rotation of 1/4 turn will not map the figures to each other.
Translation will not cause the orientation to change.
Relative to one of the short sides, one figure "leans" to the right, and the other "leans" to the left. This means a reflection is involved.
Reflection
A reflection will reverse the "lean". The line of reflection will be the perpendicular bisector of a segment between a point and its image.
Considering the two points closest to the origin, (1, 1) and (-1, -1), the perpendicular bisector of the segment between them will be the line ...
y = -x.
Checking other corresponding pairs of vertices, we see that line matches the requirement for the line of reflection.
The one transformation that maps shape A to shape B is reflection over the line y = -x.
