Question

What is the length of the mid segment of this trapezoid ; a(-2,4) b(4,3) c(4,-5) d(-2,-2)

Answer 1

Answer:

$7\ units$

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

$(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Find the midpoint e

we have

a(-2,4) and b(4,3)

substitute the given values

$e\ (\frac{-2+4}{2},\frac{4+3}{2})$

$e\ (1,3.5)$

Find the midpoint f

we have

c(4,-5), d(-2,-2)

substitute the given values

$f\ (\frac{4-2}{2},\frac{-5-2}{2})$

$f\ (1,-3.5)$

step 3

Find the length of the mid-segment ef

we have

$e\ (1,3.5)$

$f\ (1,-3.5)$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d_e_f=\sqrt{(-3.5-3.5)^{2}+(1-1)^{2}}$

$d_e_f=\sqrt{(-7)^{2}+(0)^{2}}$

$d_e_f=\sqrt{49}\ units$

$d_e_f=7\ units$