Answer: The correct option is (A) (x, y) ⇒ (y, -x).
Step-by-step explanation: We are given to select the rule that describes the transformation when parallelogram ABCD is rotated to create the image A'B'C'D'.
From the figure, we note that
the co-ordinates of the vertices of parallelogram ABCD are A(2, 5), B(5, 4), C(5, 2) and D(2, 3).
And, the co-ordinates of the vertices of the image parallelogram A'B'C'D' are A(5, -2), B(4, -5), C(2, -5) and D(3, -2).
The transformation from the co-ordinates of vertices of A'B'C'D' to A'B'C'D' is given by
A(2, 5) ⇒ A'(5, -2),
B(5, 4) ⇒ B'(4, -5),
C(5, 2) ⇒ C'(2, -5),
D(2, 3) ⇒ D'(3, -2).
So, the required transformation is (x, y) ⇒ (y, -x), which gives the rotation about the origin through 90° clockwise.
Thus, the transformation rule is described by (x, y) ⇒ (y, -x).
Option (A) is correct.
