Answer:
[tex]G = (-4,8)[/tex]
Step-by-step explanation:
Let assume that rotation is centered at origin. A rotation of 180° means that G' is the antiparallel version of G. That is:
[tex]G' = - G[/tex]
[tex](4,-8) = -G[/tex]
[tex]G = -(4,-8)[/tex]
[tex]G = (-4,8)[/tex]