Answer:
The coordinates of vertices of A'B'C'D' are:
A'(1,-8), B'(0,-4), C'(2,-1) and D'(4,-3)
Step-by-step explanation:
When a point (h,k) is roated 180 degrees about the origin it becomes (-h,-k) which means that the new point after rotation is the negative of the previous.
Given vertices are:
A(-1,8), B(0,4), C(-2,1), and D(-4,3)
The new vertices will be:

The coordinates of vertices of A'B'C'D' are:
A'(1,-8), B'(0,-4), C'(2,-1) and D'(4,-3)