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What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer.

What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B-example-1
User Keara
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1 Answer

3 votes

Answer:


(3√(13) )/(2)

Explanation:

First we have to identify the parallel sides of the trapezium.

We know that the slopes are equal for parallel lines.

Slope of (x₁,y₁) and (x₂,y₂) is given by


m = (y_(2)-y_(1))/(x_(2)-x_(1))

Slope of AB:


m_(AB) = (3-5)/(3-0)=-(2)/(3)

Slope of BC:


m_(BC) = (-2-3)/(5-3)=-(5)/(2)

Slope of CD:


m_(CD) = (2+2)/(-1-5)=-(4)/(6)=-(2)/(3)

Slope of DA:


m_(DA) = (2-5)/(-1-0)=3

We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.

The length of the midsegment = (1/2)*(length of base1 + length of base2 )

Length of the bases can be calculated using distance formula,


d= \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}

AB =
\sqrt{(3-0)^(2)+(3-5)^(2)}= √(9+4) =√(13)

CD =
\sqrt{(-1-5)^(2)+(2+2)^(2)}= √(36+16) =√(52)=2 √(13)

Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2

User Adam Sheehan
by
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