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 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 (2,2) , (-2,-2) and (-2sqrt(3),2sqrt(3)) 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.

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

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

Prove that the points (0,0) (3, sqrt(3)) and (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 (2a, 6a) (2a,4a) and (2a + sqrt3 a, 5a) are the vertices of an equilateral triangle of side 2a units.