For this case we know that the vertex P has the following coordinates:
![P=(-3,2)](https://img.qammunity.org/2023/formulas/mathematics/college/fpi86jf67zqa93xms3kf2om17yljvmjst8.png)
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 :
![P^(\prime)=(-x,-y)=(3,-2)](https://img.qammunity.org/2023/formulas/mathematics/college/ey8vkv7mrnh4nzc3f8v4imntkjch89g7ko.png)
And then the solution ofr this case would be (3,-2)