Show that the points (− 3, − 3), (3, 3) and

Let the given points be $A(-3,-3), B(3,3)$ and $C(-3 \sqrt{3}, 3 \sqrt{3})$. Now

$A B=\sqrt{(-3-3)^{2}+(-3-3)^{2}}=\sqrt{(-6)^{2}+(-6)^{2}}$

$=\sqrt{36+36}=\sqrt{72}=6 \sqrt{2}$

$B C=\sqrt{(3+3 \sqrt{3})^{2}+(3-3 \sqrt{3})^{2}}$

$=\sqrt{9+27+18 \sqrt{3}+9+27-18 \sqrt{3}}=\sqrt{72}=6 \sqrt{2}$

$A C=\sqrt{(-3+3 \sqrt{3})^{2}+(-3-3 \sqrt{3})^{2}}=\sqrt{(3-3 \sqrt{3})^{2}+(3+3 \sqrt{3})^{2}}$

$=\sqrt{9+27-18 \sqrt{3}+9+27+18 \sqrt{3}}$

$=\sqrt{72}=6 \sqrt{2}$

Hence, the given points are the vertices of an equilateral triangle.