Require to show that the given co-planar points A(2,3,2), B(4,7,6), C(1,2,3), and D(-1,-2,-1)form a parallelogram.
Find the lengths of the sides AB, BC, CD and AD of the quadrilateral ABCD
Now
AB=(4−2)2+(7−3)2+(6−2)2=4+16+16=6
BC=(1−4)2+(2−7)2+(3−6)2=9+25+9=43
CD=(−1−1)2+(−2−2)2+(−1−3)2=4+16+16=6
AD=(−1−2)2+(−2−3)2+(−1−2)2=9+25+9=43
Observe that AB=CD and BC=AD
That is opposite sides of the quadrilateral ABCD are equal.
That is the quadrilateral ABCD is a parallelogram.
Therefore, the given co-planar points form a parallelogram.
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