Q. 294.0( 5 Votes )

# Show that the points A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of a rhombus. Find its area.

Answer :

AB = √{(8 – 6)^{2} + (2 – 1)^{2}} = √{4 + 1} = √5 units

BC = √{(9 – 8)^{2} + (4 – 2)^{2}} = √{1 + 4} = √5 units

CD = √{(7 – 9)^{2} + (3 – 4)^{2}} = √{4 + 1} = √5 units

DA = √{(7 – 6)^{2} + (3 – 1)^{2}} = √{1 + 4} = √5 units

AC = √{ (9 – 6)^{2} + (4 – 1)^{2}} = √(9 + 9) = 3√2 units

BD = √{(7 – 8)^{2} + (3 – 2)^{2}} = √{1 + 1} = √2 units

Since AB = BC = CD = DA

Hence, ABCD is a rhombus

Area = 1/2 × (product of diagonals)

= 1/2 × 3√2 × √2

= 3 sq units

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