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Question
Show that the points A (3,1) , B (0,-2) , C(1,1) and D (4,4) are the vertices of parallelogram ABCD.
Solution
The points are A (3,1) , B (0,-2) , C(1,1) and D (4,4)
Join AC and BD, intersecting at O.
We know that the diagonals of a parallelogram bisect each other `".Midpoint of AC" = ((3+1)/2 , (1+1)/2) = (4/2,2/2) = (2,1) `
`"Midpoint of BD " ((0+4)/2 , (-2+4)/4) = (4/2,2/2) = (2,1)`
Thus, the diagonals AC and BD have the same midpoint
Therefore, ABCD is a parallelogram.
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