Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given. can you fill in the bottom portion?

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1 Answer
Shwetank Mauria
Mar 3, 2018

Please see below.

Explanation:

The coordinates of point #C# are #(a+b,c)#.

The coordinates of the midpoint of diagonal #bar(AC)# are #((a+b)/2,c/2)#.

The coordinates of the midpoint of diagonal #bar(BD)# are #((a+b)/2,c/2)#.

#bar(AC)# and #bar(BD)# intersect at point #E# with coordinates #((a+b)/2,c/2)#.

By the definition of midpoint, #bar(AE)~=bar(CE)# and #bar(BE)~=bar(DE)#.

Therefore diagonals #bar(AC)# and #bar(BD)# bisect each other.

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