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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