If the given figure is rotated 180° around the origin? What are the new coordinates of point Z?

(a,b) to (-a,-b)

Step-by-step explanation:

You can think of this as folding the paper horizontly and vertically, and see where the new point lies. You see that the x coordinate changes its sign  when the paper folds vertically, and the y coordinate changes its sign when folded horizontally.

But in general, if you have point (a,b) and if you rotate it 180 degrees, you just switch the signs, and you will get (-a,-b).

Ex. (-6,5) rotates 180 degrees and becomes (6,-5)