Prove that the points (2 a, 4 a), (2 a, 6 a) and 
are the vertices of an equilateral triangle.
Vertices of a triangle ABC are: A(2 a, 4 a), B(2 a, 6 a) and C
Length of side AB =
Length of side AB =
= 
= 2a units
Length of side BC =
= 
a + a units
Length of side AC =
= 
a + a units
The given vertices are not the vertices of an equilateral triangle
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