Answer:
[tex]7\ units[/tex]
Step-by-step explanation:
we have
a(-2,4), b(4,3), c(4,-5), d(-2,-2)
step 1
Plot the vertices to better understand the problem
using a graphing tool
The graph in the attached figure
step 2
Find the mid-segment parallel to ad and bc
Note : The mid-segment is parallel to the parallel bases of trapezoid
Let
e ---> midpoint segment ab
f ---> midpoint segment cd
The formula to calculate the midpoint between two points is equal to
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Find the midpoint e
we have
a(-2,4) and b(4,3)
substitute the given values
[tex]e\ (\frac{-2+4}{2},\frac{4+3}{2})[/tex]
[tex]e\ (1,3.5)[/tex]
Find the midpoint f
we have
c(4,-5), d(-2,-2)
substitute the given values
[tex]f\ (\frac{4-2}{2},\frac{-5-2}{2})[/tex]
[tex]f\ (1,-3.5)[/tex]
step 3
Find the length of the mid-segment ef
we have
[tex]e\ (1,3.5)[/tex]
[tex]f\ (1,-3.5)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]d_e_f=\sqrt{(-3.5-3.5)^{2}+(1-1)^{2}}[/tex]
[tex]d_e_f=\sqrt{(-7)^{2}+(0)^{2}}[/tex]
[tex]d_e_f=\sqrt{49}\ units[/tex]
[tex]d_e_f=7\ units[/tex]
