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

Let ABC be  an equilateral triangle with vertex A(h,k) centroid G(0,0)

AD is $\perp$to BC

Foot of perpendicular of (0,0) on the line x+y-2=0 is(1,1)

(1,1)) is  foot of median on BC

G(0,0) divide A,D in the ratio2:1

$G=\frac{2D+A}{3}\Rightarrow A=-2D=\left(-2,-2)\right)$

Vertex(-2,-2).