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

Show that the following sets of points are the vertices of an equilateral triangle :- (a,a) , (-a ,-a) and (sqrt3a, -sqrt3a) .

Show that the following sets of points are the vertices of an equilateral triangle :- (0,0), (5, 5sqrt3) and (-5,5sqrt3) .

Show that the following sets of points are the vertices of an equilateral triangle :- (3a,5a) , (3a+sqrt(3a),6a) and (3a,7a) .

Show that the following sets of points are the vertices of right isosceles triangle. :- (3,-1), (5,-1) and (3,-3).

Show that the following sets of points are the vertices of right isosceles triangle. :- (0,- 4), (3/2 -2) and (3, 0) .

By use of distance formula, prove that each of the following sets of points are vertices of a right angled triangle. :- (4, 4), (3, 5) and (-1,-1).

Two vertices of an equilateral triangle are (0, 0) and (0,2 sqrt3) . Find the third vertex.

Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertices of an equilateral triangle.

The area of an equilateral triangle with side 2 sqrt3 cm is :