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.
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
29