Q. 304.1( 10 Votes )

# 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?

Answer :

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

AC^{2} = AB^{2} + BC^{2}

Here AC^{2} = 25

But AB^{2} + BC^{2} = 15

∴ ABCD is not a rectangle

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