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marishachu [46]
3 years ago
15

What is the length of the midsegment of this trapezoid? Enter your answer in the box.

Mathematics
2 answers:
Fantom [35]3 years ago
8 0

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

<u>the answer is</u>

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

hichkok12 [17]3 years ago
4 0
I believe it is 8 because EF= \frac{AB+CD}{2} = EF= \frac{5+11}{2} =8
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