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

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.

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