[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{-1})\qquad
B(\stackrel{x_2}{2a-7}~,~\stackrel{y_2}{b+7})
\qquad
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{(2a-7)-5}{2}~~,~~\cfrac{(b+7)-1}{2} \right)=\stackrel{\stackrel{midpoint}{M}}{(6,3)}\implies \begin{cases}
\cfrac{(2a-7)-5}{2}=6\\[-0.5em]
\hrulefill\\
\cfrac{(b+7)-1}{2}=3\\[0.8em]
(b+7)-1=6\\
b+6=6\\
\boxed{b=0}
\end{cases}[/tex]
