Question

question 5 of 15
what is the length of the midsegment of this trapezoid? round your answer to the nearest tenth if necessary

Explanation:

Step1: Identify trapezoid bases

First, find the lengths of the two parallel bases of the trapezoid using the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Let the vertices be: $(-2, 6)$, $(-2, 0)$, $(4, 2)$, $(4, 5)$.
Long base (left side): $\sqrt{(-2-(-2))^2+(6-0)^2}=\sqrt{0+36}=6$
Short base (right side): $\sqrt{(4-4)^2+(5-2)^2}=\sqrt{0+9}=3$

Step2: Apply midsegment formula

The midsegment length of a trapezoid is the average of the two bases.
$\text{Midsegment length} = \frac{\text{Length of long base} + \text{Length of short base}}{2}$
$\text{Midsegment length} = \frac{6 + 3}{2}$

Step3: Calculate final value

Simplify the expression to get the length.
$\frac{9}{2}=4.5$

Answer:

4.5