Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices of a parallelogram. Show that ABCD is not a rectangle.
AB = √{(4 – 1)2 + (3 – 2)2} = √{9 + 1} = √10 units
BC = √{(6 – 4)2 + (6 – 3)2} = √{4 + 9} = √13 units
CD = √{(6 – 3)2 + (5 – 6)2} = √{9 + 1} = √10 units
DA = √{(3 – 1)2 + (5 – 2)2} = √{4 + 9} = √13 units
AB = CD and BC = DA
∴ ABCD is a parallelogram ∴
AC = √{(6 – 1)2 + (6 – 2)2} = √{25 + 16} = √41 units
For a Rectangle
AC2 = AB2 + BC2
Here AC2 = 41
But AB2 + BC2 = 23
∴ ABCD is not a rectangle
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