2012PP-II-26

答案：D
設 $P=(x,x+2)$。

$\begin{array}{rcl}
AP & = & \sqrt{(x-1)^2+(x+2-(-3))^2} \\
& = & \sqrt{2x^2+8x+26}
\end{array}$

另外，

$\begin{array}{rcl}
BP & = & \sqrt{(x-(-5))^2+(x+2-7)^2} \\
& = & \sqrt{2x^2+50}
\end{array}$

因為 $AP=PB$，可得

$\begin{array}{rcl}
2x^2+8x+26 & = & 2x^2+50 \\
8x & = & 24 \\
x& = & 3
\end{array}$

所以，$P(3,5)$。