# 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?

AB = √{(5 – 2)2 + (2 – 1)2} = √{9 + 1} = √10 units

BC = √{(6 – 5)2 + (4 – 2)2} = √{1 + 4} = √5 units

CD = √{(3 – 6)2 + (3 – 4)2} = √{9 + 1} = √10 units

DA = √{(3 – 2)2 + (3 – 1)2} = √{1 + 4} = √5 units

Since AB = CD and BC = DA

ABCD is Parallelogram

AC = √{(6 – 2)2 + (4 – 1)2} = √{16 + 9} = 5 units

For a Rectangle

AC2 = AB2 + BC2

Here AC2 = 25

But AB2 + BC2 = 15

ABCD is not a rectangle

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