Prove that the points $A (0, 0), B (0, 2)$ and $C (2, 0)$ are the vertices of an equilateral triangle.

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Solution

Using distance formula, $= \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$
$A B = \sqrt{{(0 - 0)}^{2} + {(2 - 0)}^{2}} = \sqrt{4} = 2$ units
$B C = \sqrt{{(0 - 2)}^{2} + {(0 - 0)}^{2}} = \sqrt{4} = 2$ units
$C A = \sqrt{{(0 - 0)}^{2} + {(2 - 0)}^{2}} = \sqrt{4} = 2$ units
$∴ A B = B C = C A$
Hence the given triangle form an equilateral triangle.

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