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IceJOKER [234]
3 years ago
7

Three vertices of the trapezoid are A(4d,4e), B(4f,4e), and C(4g,0). The fourth vertex lies on the origin. Find the midpoint of

the midsegment of the trapezoid.

Mathematics
1 answer:
satela [25.4K]3 years ago
8 0
We have that

point C and point D have y = 0-----------> (the bottom of the trapezoid).

point A and point B have y = 4e ---------- > (the top of the trapezoid)

the y component of  midpoint would be halfway between these lines
 y = (4e+ 0)/2 = 2e. 

<span>the x component of the midpoint of the midsegment would be halfway between the midpoint of AB and the midpoint of CD.

x component of midpoint of AB is (4d + 4f)/2.
x component of midpoint of CD is (4g + 0)/2 = 4g/2.
x component of a point between the two we just found is
[(4d + 4f)/2 + 4g/2]/2 = [(4d + 4f + 4g)/2]/2 = (4d + 4f + 4g)/4 = d + f + g. 

</span>therefore

the midpoint of the midsegment is (d + f + g, 2e)
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