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(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(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.

Prove that the points (2a, 4a), (2a, 6a) and (2a+ sqrt(3) a, 5a) are the vertices of an equilateral triangle.

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

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

Show that the points (1,1),(-1,-1) and ( -sqrt3,sqrt3 ) are the vertices of an equilateral triangle.

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Prove that the points (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral triangle.