Question 1120693: A, B, C, D have coordinates (0,1,3), (4,5,-5), (-3,0,-1) and (7,5,4) respectively.
Justify whether ABCD is a parallelogram.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A, B, C, D have coordinates (0,1,3), (4,5,-5), (-3,0,-1) and (7,5,4) respectively.
Justify whether ABCD is a parallelogram.
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Assuming the points are in order around the figure:
Find the lengths of the pairs, AB and CD, and of BC and AD.
AB --> sqrt(4^2 + 4^2 + 8^2) = sqrt(80)
CD --> sqrt(10^2 + 5^2 + 5^2) = sqrt(150)
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The 2 sides are not equal, so it cannot be a parallelogram.
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If not labelled in order:
AC --> sqrt(3^2 + 1 + 4^2) = 5
BD --> sqrt(3^2 + 0 + 9^2) = sqrt(90)
Not a parallelogram.
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