Answer
$(5,-4)$
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 $(
12,6
)$ and the other endpoint is $(
19,16
)$ are
\begin{array}{l}\require{cancel}
\dfrac{m+19}{2}=12
\\\text{AND}\\
\dfrac{n+16}{2}=6
.\end{array}
Solving these equations separately results to
\begin{array}{l}\require{cancel}
m+19=2(12)
\\\\
m+19=24
\\\\
m=24-19
\\\\
m=5
\\\text{AND}\\
n+16=2(6)
\\\\
n+16=12
\\\\
n=12-16
\\\\
n=-4
.\end{array}
Hence, the missing endpoint is $
(5,-4)
.$