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