Show that the points A(1, 1), B(-1, -1) and C(-√3, √3) are the vertices of an equilateral triangle each of whose sides is 22 units.
Given: The 3 points are A(1, 1), B(-1, -1) and C(-√3, √3).
AB 
= 2√2 units …..(1)
BC 
= 2√2 units …..(2)
AC 
= 2√2 units …..(3)
From equations 1, 2 and 3, we have
AB = BC = AC = 2√2 units.
Therefore, Δ ABC is an equilateral triangle each of whose sides is 2√2 units.
Hence, proved.
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