Matrix matching: Consider the triangle whose vertices are (6, 0), (0, 6) and (6, 6)

A) Centroid $G=(\frac{6+0+6}{3},\frac{0+6+6}{3})$

$=(4,4)$.

B) Circumcentre $\left(S\right)$: The point which divides $\stackrel{\rightharpoonup }{OG}$ in the $3:1$ externally

$=(\frac{3\left(4\right)-1\left(6\right)}{3-1},\frac{3\left(4\right)-1\left(6\right)}{3-1})$

$S=(3,3)$.

C) Orthocenter of the triangle having vertices $(\alpha ,\beta ),(\beta ,\alpha ),(\alpha ,\alpha )$ is $(\alpha ,\alpha )$

Orthocenter $O=(6,6)$.

D) Nine point centre $\left(N\right)=(\frac{6+3}{2},\frac{6+3}{2})$

$=(\frac{9}{2},\frac{9}{2})$