Answer
$(-2,7)$
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 $(
-9,8
)$ and the other endpoint is $(
-16,9
)$ are
\begin{array}{l}\require{cancel}
\dfrac{m+(-16)}{2}=-9
\\\text{AND}\\
\dfrac{n+9}{2}=8
.\end{array}
Solving these equations separately results to
\begin{array}{l}\require{cancel}
m-16=2(-9)
\\\\
m-16=-18
\\\\
m=-18+16
\\\\
m=-2
\\\text{AND}\\
n+9=2(8)
\\\\
n+9=16
\\\\
n=16-9
\\\\
n=7
.\end{array}
Hence, the missing endpoint is $
(-2,7)
.$
