a
$\Delta=\frac{1}{2}\left|\begin{array}{lll}{2 k} & {k} & {1} \\ {k} & {2 k} & {1} \\ {k} & {k} & {1}\end{array}\right|=\pm 18$
$\frac{k^{2}}{2}\left|\begin{array}{lll}{2} & {1} & {1} \\ {1} & {2} & {1} \\ {1} & {1} & {1}\end{array}\right|=\pm 18$
$\frac{\mathrm{k}^{2}}{2}[2(2-1)-1(1-1)+1(1-2)]=\pm 18$
$\frac{\mathrm{k}^{2}}{2}=\pm 18 \Rightarrow \mathrm{k}=6$
Centroid $\left(\frac{12+6+6}{3}, \frac{6+12+6}{3}\right)$
$=(8,8)$