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

Let the vertices B and C lie on the given line. Then, OD=222=2 (perpendicular distance from origin=ca2+b2) Let equation od OD be y=mx,  since slope is perpendicular to x+y=22  is 1, ∴equation is x=y solving the two equations we get D (2,2)= Also, BD=OD×tan⁡60∘=23 for the coordinates of B and C . Slope of the given line is -1, slope of OD is 1 ,hence angle of inclination is 450Using parametric equation of line, we get     x−21/2=y−21/2=±23 or     C≡(2+6,2−6) and     B≡(2−6,2+6)