Answer:
7.5
Step-by-step explanation:
A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.
Given vertices of trapezoid STUV:
- S = (0, 0)
- T = (2, 7)
- U = (6, 10)
- V = (8, 6)
The parallel bases of the trapezoid are TU and SV.
Find the lengths of TU and SV using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]
Substitute the found lengths of the bases into the midsegment formula:
[tex]\implies M=\dfrac{5+10}{2}[/tex]
[tex]\implies M=\dfrac{15}{2}[/tex]
[tex]\implies M=7.5[/tex]
The length of the midsegment is 7.5.
