contestada

If the parallel sides of a trapezoid are contained by the lines y=-1/4x+5 and y=-1/4x-1, find the equation of the line that contains the midsegment.

Respuesta :

[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]

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