Answer: The correct option is (C). (-2, 2).
Step-by-step explanation: Given that the co-ordinates of the vertices of parallelogram ABCD are A(0, 1), B(1, 3), C(4, 3), and D(3, 1). The parallelogram ABCD is translated 2 units to the right and 3 units down and then rotated 180 clockwise around the origin.
We are to find the co-ordinates of the vertex A after the transformation.
We know that if the point (x, y) is translated a units right and b units down, then its new co-ordinates will be (x + a, y - b).
So, the co-ordinates of point A after translation of 2 units to the right and 3 units down are
(0 + 2, 1 - 3) = (2, -2).
Now, a rotation of 180° clockwise will change the co-ordinates (x, y) to (-x, -y).
Therefore, the final co-ordinates of point A are
(2, -2) ⇒ (-2, 2).
Thus, the new co-ordinates of A are (-2, 2).
Option (C) is CORRECT.
