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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