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