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

If A(1, 1), B(sqrt(3)+1,2) and C(sqrt(3), sqrt(3)+2) be three vertices of a square, then the diagonal through B is

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.

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.,

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

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

If the points (1, 1), (-1, -1) and (-sqrt(3),k) are vertices of a equilateral triangle then the value of k will be : (a)1 (b)-1 (c) sqrt3 (d) -sqrt3

If A(1,-1,2),B(2,1,-1)C(3,-1,2) are the vertices of a triangle then the area of triangle ABC is (A) sqrt(12) (B) sqrt(3) (C) sqrt(5) (D) sqrt(13)