Show that the following points taken in order form an equilateral triangle in each case .
(i) `A(2,2), B(-2,-2), C-2sqrt(3),2sqrt(3))` (ii) `A(sqrt(3),2),B(0,1),C(0,3)`

Show that the following points form an equilateral triangle A(a, 0), B(-a, 0), C(0, a sqrt(3))

Show that the folloiwng points taken in order form an isosceles triangle . (i) A(5,4), B (2,0),C(-2,3) (ii) A(6,4),B(-2,-4),C(2,10)

One vertex of an equilateral triangle is (2,2) and its centroid is (-2/sqrt3,2/sqrt3) then length of its side is

The triangle with vertices A (2,4), B (2,6) and C ( 2 + sqrt3 , 5) is

Which of the following sets of points form an equilateral triangle? (a) (1,0),(4,0),(7,-1) (b) (0,0),(3/2,4/3),(4/3,3/2) (c) (2/3,0),(0,2/3),(1,1) (d) None of these

Prove that the points (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral triangle.

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . An equilateral triangle A B C is constructed. The possible coordinates of vertex C (a) (2(1-(3sqrt(3))/4),3/2(1-4/(sqrt(3)))) (b) (-2(1+sqrt(3)),3/2(1-sqrt(3))) (c) (2(1+sqrt(3)),3/2(1+sqrt(3))) (d) (2(1+(3sqrt(3))/4),3/2(1+4/(sqrt(3))))

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4/sqrt(3) units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-2/(sqrt(3)),2) (b) (0,0) (c) (2/(sqrt(3)),2) (d) (0,4)