The image of the centroid of the triangle whose ortho centre is at origin and the circum centre at 3,3  in the line which is equally inclined with axes in the first quadrant is

In any triangle the centroid G divides the line segment joining ortho center  Oand the circum centre S in the ratio  2:1It implies  G=mx2+nx1m+n,my2+ny1m+n=23+101+2,23+101+2=2,2 Equation of the line which is equally inclined, means making equal angles with axes in the first quadrant is  x=yThe image of the point Px1,y1 in the line   x=yis   y1,x1The image of  G=2,2 in the line  x=y is  2,2