Answer: The correct option is (B) (5, 2).
Step-by-step explanation: Given that the co-ordinates of the vertices of pentagon ABCDE are A(-2, 4), B(-6, 2), C(-5, -2), D(1, -2) and E(2, 2).
We are to find the co-ordinates of the point C', if the pentagon ABCDE is rotated 180° around the origin to create pentagon A'B'C'D'E'.
We know that a rotation of 180° changes the co-ordinates of a point (x, y) according to the following rule:
(x, y) ⇒ (-x, -y).
Therefore, the vertices of pentagon ABCD will transform to the vertices of pentagon A'B'C'D'E' as follows:
A(-2, 4) ⇒ A'(2, -4),
B(-6, 2) ⇒ B'(6, -2),
C(-5, -2) ⇒ C'(5, 2),
D(1, -2) ⇒ D'(-1, 2),
E(2, 2) ⇒ E'(-2, -2).
Thus, the co-ordinates of the point C' are (5, 2).
Option (B) is correct.
