Answer :

For this case we know that the vertex P has the following coordinates:

[tex]P=(-3,2)[/tex]

And we want to find the coordinates after rotate 180 degrees about the origin we assume that the translation is anticlockwise so then we just need to do the following :

[tex]P^{\prime}=(-x,-y)=(3,-2)[/tex]

And then the solution ofr this case would be (3,-2)