Triangle $OAB$ has $O=(0,0)$, $B=(0,10)$, and $A$ in the first quadrant. In addition, $\angle BAO=90^{\circ }$ and $\angle AOB=45^{\circ }$. Suppose that $OA$ is rotated $180^{\circ }$ about $O$. What are the coordinates of the image of $A$?