The centroid of an equilateral triangle is(0,0) . If two vertices of the triangle of the lie on x+y=22 then one of them will have its coordinates

Let the vertices B and C lie on the given line.ThenOD=222=2 . Equation of OD isy=x⇒x=y=2 (for point D)Also, BD=OD×tan600=23 for the coordinates of B and C. using parametric equation of line, we getx−2−12=y−212=±23⇒C≡(2+6,2−6)And B≡(2−6,2+6)