Question

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The midsegment of a trapezoid is the segment that is created by joining the midpoints of the legs of a trapezoid.
1) Find the coordinates of the endpoints of the midsegment KL as shown.
2) Prove that the midsegment of a trapezoid is half the sum of the bases.

Answer 1

Explanation:

distance between 2 points = d = √(x2 - x1)² + (y2 - y1)²

JI = √(3--2)² + (4-4)² = √5² = 5

GH = √(5--5)² + (0-0)² = √10² = 10

sum of bases JI + GH = 10 + 5 = 15

1/2 sum of bases = 15/2

JG = √(-5--2)² + (0-4)² = √9 + 16 = √25 = 5

JK = 5/2 = KG

IH = √(5-3)² + (0-4)² = √4 + 16 = √20 = 2√5

IL = 2√5/2 = √5 = LH

coordinates of K: (-5+-2)/2, (0+4)/2 = (-7/2, 2)

coordinates of L: (5+3)/2, (0+4)/2 = (4, 2)

KL = √(4--7/2)² + (2-2)² = 15/2

Answer 2

K equals (-7/2,2) and L equals (4,2) bc of midpoint formula. J’s x coordinate plus I’s x coordinate equal 1. Their y-coordinate equals 8. The sum of K and L’s x coordinate is 1/2 which is half of 1. Their y coordinate sum equals 4 which is half of 8.