Prove that A(1, 1), B(-1,-1),`C(-sqrt3,sqrt3)`are the points of vertices of an equilateral triangle.

Show that the point A(0,1,2), B(2,-1,3) and C(1,-3,1) are vertices of an isosceles right angled triangle.

If the three points (0, 1), (0, -1) and (x, 0) are vertices of an equilateral triangle, then the values of x are

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

If |z_(1)|= |z_(2)|= |z_(3)|=1 and z_(1) , z_(2), z_(3) are represented by the vertices of an equilateral triangle then which of the following is true?

The pointsA(0,0), B(10,0),C (5,5sqrt3) are the vertices of the triangle ABC.Find AB,BC,AC and prove that the triangle is equilateral.

Given A(1,1,1),B(1,2,3),C(2,3,1) are the vertices of triangleABC a triangle. Find the area of the triangleABC .

Consider the points A (1,2,3), B(2,3,1) and C(3,1,2) Prove that DeltaABC is equilateral

An equilateral triangle is inscribed in the parabola y^2 =4ax whose one vertex is at the vertex of the parabola if 1 cms is the side of the equilateral triangle prove that the length of each altitude of the triangle is (1sqrt3)/2 cms

Consider the triangle ABC with vertices A(1,1,1), B(1,2,3) and C(2,3,1).Hence find the area of the triangle.