Answer
$B(5,-2)$
Work Step by Step
Step 1.
See graph below for points $A(-1,8), M(2,3)$ where M is the midpoint of AB.
Step 2.
Recall the Midpoint formula:
The midpoint $M$of the points $P(x_1, y_1)$ and $Q(x_2,y_2)$ is:
$M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
Let us assume the coordinates of point $B$ are $(x,y)$.
Since $M=(2, 3)$ is the midpoint of $A=(-1, 8)$ and $B=(x,y)$, then using the Midpoint Formula we have:
$2=\dfrac{x+(-1)}{2}$ and $3=\dfrac{y+8}{2}$
Solve each equation:
$\begin{align*}
2&=\frac{x+(-1)}{2}\\
2(2)&=x+(-1)\\
4&=x-1\\
4+1&=x\\
5&=x\end{align*}$
$\begin{align*}
3&=\frac{y+8}{2}\\
2(3)&=y+8\\
6&=y+8\\
6-8&=y\\
-2&=y\end{align*}$
Therefore, $B=(x,y)=(5, -2)$.
