Question

What is the length of the midsegment of this trapezoid?

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Answer 1

I believe it is 8 because $EF= \frac{AB+CD}{2} = EF= \frac{5+11}{2} =8$

Answer 2

we know that

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides of the trapezoid, and is parallel to the pair of parallel sides.

In this problem

the two non-parallel sides of the trapezoid are AD and BC

Step 1

Find the midpoint side AD

Let

E-------> the midpoint AD

$A(2,4)\ D(-2,-1)$

Find the x-coordinate of the midpoint AD

$x=\frac{2-2}{2}=0$

Find the y-coordinate of the midpoint AD

$y=\frac{4-1}{2}=1.5$

the point E is equal to $(0,1.5)$

Step 2

Find the midpoint side BC

Let

F-------> the midpoint BC

$B(7,4)\ C(9,-1)$

Find the x-coordinate of the midpoint BC

$x=\frac{9+7}{2}=8$

Find the y-coordinate of the midpoint BC

$y=\frac{4-1}{2}=1.5$

the point F is equal to $(8,1.5)$

Step 3

Find the distance EF

we know that

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

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

we have

$E(0,1.5)\ F(8,1.5)$

substitute the values

$d=\sqrt{(1.5-1.5)^{2}+(8-0)^{2}}$

$d=8\ units$

therefore

the answer is

the length of the midsegment of the trapezoid is $8\ units$