Answer
$P_{2}=(1,2)$
Work Step by Step
The midpoint $M=(x,y)$ of the line segment from $P_{1}=(x_{1},y_{1})$ to $P_{2}=(x_{2},y_{2})$ is
$M=(x,y)=(\displaystyle \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
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Given
$P_{1}=(x_{1},y_{1})=(-3,6)$
$P_{2}=(x_{2},y_{2}),$
$M=(\displaystyle \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) =(-1,4)$
$ \begin{aligned}
& & & & & & \\
\frac{-3+x_{2}}{2} & =-1 & /\times 2 & ... & \frac{6+y_{2}}{2} & =4 & /\times 2\\
-3+x_{2} & =-2 & /+3 & & 6+y_{2} & =8 & /-6\\
x_{2} & =1 & & & y_{2} & =2 &
\end{aligned}$
$P_{2}=(1,2)$
