The vertices of a triangle are (-2, 0), (2, 3) and (1, -3) is the triangle equilateral, isosceles or scalene?

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Solution

Let $A (2, 0), B (2, 3)$ and $C (1, 3)$
Distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ can be calculated using the formula
$\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$
Distance between the points AB $= \sqrt{{(2 + 2)}^{2} + {(3 - 0)}^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5$

Distance between the points BC $= \sqrt{{(1 - 2)}^{2} + {(- 3 - 3)}^{2}} = \sqrt{1 + 37} = \sqrt{37}$

Distance between the points AC $= \sqrt{{(1 + 2)}^{2} + {(- 30)}^{2}} = \sqrt{9 + 9} = \sqrt{18}$
Since all the sides are of different length, the triangle is a scalene triangle.

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