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What is the length of the midsegment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?

What is the length of the midsegment of a trapezoid whose vertices are I(-3, -5), J-example-1
User John Snelson
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1 Answer

17 votes
17 votes

Answer:

the answer will be 4.75 units

Explanation:

explained

The midsegment of a trapezoid is a line segment that connects the midpoints of the nonparallel sides of the trapezoid. To find the length of the midsegment, we need to first find the midpoints of the sides IJ and KL.

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. We can find the midpoint of a line segment by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.

The coordinates of the endpoints of the side IJ are (-3, -5) and (8, -5), so the midpoint of this side is:

((-3 + 8)/2, (-5 + (-5))/2) = (2.5, -5)

The coordinates of the endpoints of the side KL are (-3, -9) and (3, -9), so the midpoint of this side is:

((-3 + 3)/2, (-9 + (-9))/2) = (0, -9)

To find the length of the midsegment, we can use the distance formula to find the distance between the two midpoints:

sqrt((2.5 - 0)^2 + (-5 - (-9))^2) = sqrt(2.5^2 + 4^2) = sqrt(6.25 + 16) = sqrt(22.25) = 4.75

Therefore, the length of the midsegment of the trapezoid is approximately 4.75 units.

User Siavosh
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