The correct option is A (−2,−2)
Let the vertices of the triangle is A,B,C and D be the mid point of BC and BC lies in the line x+y−2=0
∴A will lie in 3rd quadrant.
∵ the triangle is equilateral the centroid G(0,0) is also orthocenter and median AD is also its altitude and G divides it in the ratio 2:1.
Let the coordinates of A be (a,b), then
Equation of the line perpendicular to BC and passing through origin is x=y and A lie on it.
Hence, coordinates of A is (−2,−2).