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What is the length of the midsegment of a trapezoid whose verticals are E(-7,6), F(-2,5)

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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 of a trapezoid, you need to first find the coordinates of the midpoints of the nonparallel sides of the trapezoid.

The coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:

(x1 + x2)/2, (y1 + y2)/2

In the given trapezoid, the coordinates of the midpoint of the line segment E(-7,6) and F(-2,5) are:

(-7 + -2)/2, (6 + 5)/2 = -4.5, 5.5

To find the length of the midsegment, you need to use the distance formula to find the distance between the two midpoints:

sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of the two midpoints, we get:

sqrt((-4.5 - (-7))^2 + (5.5 - 6)^2) = sqrt(2.5^2 + (-0.5)^2) = sqrt(6.25 + 0.25) = sqrt(6.5) = 2.54

So the length of the midsegment of the given trapezoid is approximately 2.54.

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