Answer
$(-5,3)$
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 $(
-7,6
)$ and the other endpoint is $(
-9,9
)$ are
\begin{array}{l}\require{cancel}
\dfrac{m-9}{2}=-7
\\\text{AND}\\
\dfrac{n+9}{2}=6
.\end{array}
Solving these equations separately results to
\begin{array}{l}\require{cancel}
m-9=2(-7)
\\\\
m-9=-14
\\\\
m=-14+9
\\\\
m=-5
\\\text{AND}\\
n+9=2(6)
\\\\
n+9=12
\\\\
n=12-9
\\\\
n=3
.\end{array}
Hence, the missing endpoint is $
(-5,3)
.$
