Show that the following points are the vertices of a square:
A(0, – 2), B(3, 1), C(0, 4) and D(– 3, 1)
AB = √{(3 – 0)2 + (1 – (– 2))2} = √{9 + 9} = √18 units
BC = √{(0 – 3)2 + (4 – 1)2} = √{9 + 9} = √18 units
CD = √{(– 3 – 0)2 + (1 – 4)2} = √{9 + 9} = √18 units
DA = √{(– 3 – 0)2 + (1 – (– 2))2} = √{9 + 9} = √18 units
AC = √{ (4 – (– 2))2} = √{36} = 6 units
BD = √{(– 3 – 3)2 + (1 – 1)2} = √{36} = 6units
Since AB = BC = CD = DA and AC = BD
∴ ABCD is a square.
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