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

Question

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

Infinity Learn · Accepted Answer

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  $$2$$,$$2$$

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

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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

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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