KEAM 2015 Math Paper

The circumcentre O, centroid G and orthocentre O ' of a triangle are collinear.
G divides O′O in the ratio 2: 1
Let the coordinates of G be (x,y).
Then (‌

2×5+1×2

2+1

,‌

2×5+1×2

2+1

)
=(x,y)⇒(x,y)=(4,4)
Hence, coordinates of centroid are (4,4)