jmc

Applying the midpoint formula gives us $$\left(\frac{-9+x}{2},\frac{1+y}{2}\right)=(3,-5).$$Solving $\frac{-9+x}{2}=3$ for $x$ and solving $\frac{1+y}{2}=-5$ for $y$, we find the coordinates $(x,y)$ to be $\boxed{(15,-11)}$.