One vertex of the equilateral triangle with centroid at the origin and one side as `x+y-2=0` is :

Options

A. (-1,1)
B. (2,2)
C. (-2,-2)
D. none of these

Explanation

Since the triangle is equilateral . Therefore , centroid coincides with the circumcentre and orthocentre . The equation of the perpendicular bisector of x + y - 2= 0 and passing through the centroid (0,0) is x - y = 0 .
The vertex of the triangle must lie on x- y = 0 and the origin and the vertex must lies on the same side of x + y - 2 = 0. So we can choose (-2,-2) as the vertex .