Prove that the points `A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(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 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 A(1, -3), B (-3, 0) and C(4, 1) are the vertices of an isosceles right- angled triangle. Find the area of the triangle.

Prove that the points (-3,\ 0),\ (1,\ -3) and (4,\ 1) are the vertices of an isosceles right-angled triangle. Find the area of this triangle.

Prove that the points A (1,-3) B (-3,0) and C(4,1) are the vertices of an isosceles right angle triangle. Find the area of the triangle.

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

If the point (0,0),(2,2sqrt(3)), and (p,q) are the vertices of an equilateral triangle, then (p ,q) is

Prove that the points A(1,−3),B(−3,0) and C(4,1) are the vertices of a right angled Isosceles triangle

Prove that the points O(0,0,0), A(2.0,0), B(1,sqrt3,0) and C(1,1/sqrt3,(2sqrt2)/sqrt3) are the vertices of a regular tetrahedron.,

If A(1,1), B(sqrt3+1,2) and C(sqrt3,sqrt3+2) are three vertices of a square, then the diagonal through B is