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

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 lie on the same side of x + y - 2 = 0. So, we can choose (- 2, - 2) as the vertex