Show that the following points are the vertices of a square:
A(3, 2), B(0, 5), C(– 3, 2) and D(0, – 1)
AB = √{(0 – 3)2 + (5 – 2)2} = √{9 + 9} = √18 units
BC = √{(– 3 – 0)2 + (2 – 5)2} = √{9 + 9} = √18 units
CD = √{(0 – (– 3))2 + (– 1 – 2)2} = √{9 + 9} = √18 units
DA = √{(0 – 3)2 + (– 1 – 2)2} = √{9 + 9} = √18 units
AC = √{(– 3 – 3)2} = √36 = 6 units
BD = √{(– 1 – 5)2} = √36 = 6 units
Since AB = BC = CD = DA and AC = BD
∴ ABCD is a square.
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