Answer
$Q(11,-4)$
Work Step by Step
To find the midpoint between points $(x_1,y_1)$ and $(x_2,y_2)$, we use the midpoint formula:
$\displaystyle Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
We have the two points, $P(5,8)$ and $Q(x,y)$. The midpoint is $M(8,2)$. Thus we have:
$\displaystyle Midpoint=(\frac{5+x}{2},\ \frac{8+y}{2})=(8,2)$
We solve for $x$:
$\frac{5+x}{2}=8$
$5+x=16$
$x=11$
And for $y$:
$\frac{8+y}{2}=2$
$8+y=4$
$y=-4$
Therefore, the point Q is: $(11,-4)$