Answer
$(-3,6)$
Work Step by Step
Let $(m,n)$ be the missing endpoint. Using $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, then the coordinates of the missing endpoint, given that the midpoint is $(
5,8
)$ and the other endpoint is $(
13,10
)$ are
\begin{array}{l}\require{cancel}
\dfrac{m+13}{2}=5
\\\text{AND}\\
\dfrac{n+10}{2}=8
.\end{array}
Solving these equations separately results to
\begin{array}{l}\require{cancel}
m+13=2(5)
\\\\
m+13=10
\\\\
m=10-13
\\\\
m=-3
\\\text{AND}\\
\dfrac{n+10}{2}=8
\\\\
n+10=2(8)
\\\\
n+10=16
\\\\
n=16-10
\\\\
n=6
.\end{array}
Hence, the missing endpoint is $
(-3,6)
.$