Question

If pentagon ABCDE is rotated 180 degrees around the origin to create pentagon A’ B’ C’ D’ E’, what is the ordered pair of point C?

Answer 1

You haven't provided the original coordinates or the figure, therefore, I cannot give an exact answer. However, I will help you with the concept.

For rotation 180° about the origin, the signs of both the x any y coordinates are changed.
This can be modeled as follows:
(x,y) ......> rotation 180° about the origin ........> (-x,-y)

Examples:
(1,2) .......> rotation 180° about the origin ........> (-1,-2)
(2,-19) ....> rotation 180° about the origin ........> (-2,19)
(-3,-8) .....> rotation 180° about the origin ........> (3,8)
(-5,7) ......> rotation 180° about the origin ........> (5,-7)

Based on the above, all you have to do to get the coordinates of C' is change the signs of both the x and y coordinates

Hope this helps :)