Answer:
C
Step-by-step explanation:
Consider all options.
A. A reflection across the line x=2 gives us the parallelogram A'B'C'D' (see first attached diagram) with vertices A'(4,0), B'(4,6), C'(0,4) and D'(0,-2). As you can see this is not the same parallelogram as parallelogram ABCD.
B. A reflection across the line y=2 gives us the parallelogram A''B''C''D'' (see first attached diagram) with vertices A''(0,4), B''(0,-2), C''(4,0) and D''(4,6). As you can see this is not the same parallelogram as parallelogram ABCD.
C. A rotation of 180° about the point (2,2) gives us the same parallelogram ABCD (see second attached diagram), because the image of A is C, the image of B is D, the image of C is A and the image of D is B.
D. A rotation of 180° about the point (0,0) gives us the parallelogram A'''B'''C'''D''' (see second attached diagram) that differs from parallelogram ABCD.
