3. Given $A(3,-1), B(-1,4), C(1,-6)$, find a point $P$ inside $\triangle A B C$ such that $P A^{2}+P B^{2}+P C^{2}$ is minimized. Then the coordinates of point $P$ are $\qquad$.
Let $P(x, y)$. Then
$$
\begin{array}{l}
P A^{2}+P B^{2}+P C^{2} \\
=3 x^{2}+3 y^{2}-6 x+6 y+64 \\
=3(x-1)^{2}+3(y+1)^{2}+58 .
\end{array}
$$

Therefore, $P(1,-1)$.