[tex]\bf \textit{midsegment of a trapezoid}\\\\
m=\cfrac{a+b}{2}\quad
\begin{cases}
a,b=\stackrel{bases}{parallel~sides}\\
----------\\
a=-\frac{1}{4}x+5\\\\
b=-\frac{1}{4}x-1
\end{cases}
\\\\\\
m=\cfrac{\left( \stackrel{a}{-\frac{1}{4}x+5} \right)~~+~~\left(\stackrel{b}{-\frac{1}{4}x-1} \right)}{2}
\\\\\\[/tex]
[tex]\bf m=\cfrac{\left( \frac{-x+20}{4} \right)~~+~~\left(\frac{-x-4}{4} \right)}{2}\implies m=\cfrac{\frac{-x+20-x-4}{4}}{2}
\\\\\\
m=\cfrac{\frac{-2x+16}{4}}{2}\implies m=\cfrac{\frac{-x+8}{2}}{2}\implies m=\cfrac{\frac{-x+8}{2}}{\frac{2}{1}}\implies m=\cfrac{-x+8}{2}\cdot \cfrac{1}{2}
\\\\\\
m=\cfrac{-x+8}{4}\implies m=\cfrac{8-x}{4}[/tex]
