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kozerog [31]
2 years ago
8

Find the length of midsegment YZ in trapezoid ABCD when A(-5,-6) B(-6,-2) C(-4,0) and D(3,2)

Mathematics
1 answer:
Luda [366]2 years ago
7 0

Answer:

Option C

Step-by-step explanation:

Since, Y and Z are the midpoints of sides AB and CD of the given trapezoid.

Segment YZ will the midsegment of trapezoid ABCD.

By the theorem of midsegment,

m(YZ) = \frac{1}{2}(AD+BC)

By using expression for the length of a segment between two points,

Length of a segment = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Distance between two points A(-5, -6) and D(3, 2),

AD = \sqrt{(3+5)^2+(2+6)^2}

AD = \sqrt{64+64}

AD = \sqrt{128}

AD = 8\sqrt{2}

Distance between B(-6, -2) and C(-4, 0)

BC = \sqrt{(-6+4)^2+(-2-0)^2}

BC = \sqrt{8}

BC = 2\sqrt{2}

Therefore, m(YZ) = \frac{1}{2}(8\sqrt{2}+2\sqrt{2})

                             = \frac{1}{2} (10\sqrt{2})

                             = 5\sqrt{2}

Option C will be the answer.

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