Show that the points (-3, -3), (3, 3) and `(-3sqrt(3), 3sqrt(3))` are the vertices of an equilateral triangle.

Prove that the points (a, a), (-a, -a) and (-asqrt(3), asqrt(3)) are the vertices of an equilateral triangle.

Prove that the points (a, a), (-a, -a) and (-asqrt(3), asqrt(3)) are the vertices of an equilateral triangle.

Show that the point A(a,a), B(-a,-a) and C (-sqrt(3)a, sqrt(3) a) are the vertices of an equilateral triangle.

Show that the points (a , a),(-a ,-a) and (-sqrt(3)a ,sqrt(3)a) are the vertices of an equilateral triangle. Also, find its area.

Show that the points (2,2) , (-2,-2) and (-2sqrt(3),2sqrt(3)) are the vertices of an equilateral triangle .

Prove that the points A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(3)) are the vertices of an equilateral triangle.

Show that the points O(0, 0), A(3, sqrt(3)) "and "B(3, -sqrt(3)) are the vertices of an equilateral triangle. Find the area of this triangle.

Show that the points (a,a),(-a,-a) and (-sqrt(3)a,sqrt(3)a) are the vertices of an equilateral triangle.Also,find its area.

Show that the points A(1, 1), B(-1, -1) and C(-sqrt3, sqrt3) are the vertices of an equilateral triangle each of whose sides is 2sqrt2 units.