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Question

Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle ?

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Solution

Let A(2,1), B(5,2), C(6,4) and D(3,3) be the vertices of a parallelogram
ABCD. Since, the diagonals of a parallelogram bisect each other.AC2=(62)2+(41)2
=(4)2+(3)2
=16+9=25
BC2=(65)2+(42)2
=(1)2+(2)2
=1+4=5
AB2=(52)2+(21)2
=(3)2+(1)2=9+1=10
DC2=(63)2+(43)2
=(3)2+(1)2
=9+1=10
AD2=(32)2+(31)2
=(1)2+(2)2
=1+4=5
Since BC=AD and DC=AB, ABCD is a parallelogram.
AB2+BC2=10+5=15
AB2+BC2AC2
ΔABC is not right angled. Therefore parallelogram ABCD is not a rectangle.


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