Show that the following points are the vertices of a square:
A(6, 2), B(2, 1), C(1, 5) and D(5, 6)
AB = √{(2 – 6)2 + (1 – 2)2} = √{16 + 1} = √17 units
BC = √{(1 – 2)2 + (5 – 1)2} = √{1 + 16} = √17 units
CD = √{(5 – 1)2 + (6 – 5)2} = √{16 + 1} = √17 units
DA = √{(5 – 6)2 + (6 – 2)2} = √{16 + 1} = √17 units
AC = √{(1 – 6)2 + (5 – 2)2} = √{25 + 9} = √34 units
BD = √{(5 – 2)2 + (6 – 1)2} = √{25 + 9} = √34units
Since AB = BC = CD = DA and AC = BD
∴ ABCD is a square.
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