Question

prove that (-3. -2), (3,2) and (-2$\sqrt{3}$, 3$\sqrt{3}$) form an equlateral triangle on joining them in that order.

Answer 1

Let the points be designated as $A(-3,-2); B(3,2); C(-2\sqrt{3},3\sqrt{3}).$
Then, we need length of sides, using $L=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$
$BC=\sqrt{52}$, $CA=\sqrt{52}$, $AB=\sqrt{52}.$
Hence, $BC=CA=AB=\sqrt{52}.$
All the sides are equal, therefore vertices A, B, C form an equilateral triangle.