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

`7\ units`

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

`((x1+x2)/(2),(y1+y2)/(2))`

Find the midpoint e

we have

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

substitute the given values

`e\ ((-2+4)/(2),(4+3)/(2))`

`e\ (1,3.5)`

Find the midpoint f

we have

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

substitute the given values

`f\ ((4-2)/(2),(-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=√(49)\ units`

`d_e_f=7\ units`