Let \[A\left( \alpha ,\frac{1}{\alpha } \right),B\left( \alpha ,\frac{1}{\beta } \right),C\left( \gamma ,\frac{1}{\gamma } \right)\] be the vertices of a \[\Delta ABC,\] where \[\alpha ,\beta \] are the roots of the equation \[{{x}^{2}}-6{{p}_{1}}x+2=0,\,\,\beta ,\,\,\gamma \]\[{{x}^{2}}-6{{p}_{1}}x+2=0,\beta ,\gamma \] are the roots of the equation \[{{x}^{2}}-6{{p}_{2}}x+3=0\] and \[\gamma ,\alpha \] are the roots of the equation \[{{x}^{2}}-6{{p}_{3}}x+6=0,{{p}_{1}},{{p}_{2}},{{p}_{3}}\] being positive. Then, the coordinates of the centroid of \[\Delta ABC\] is

• A. \[\left( 1,\frac{11}{18} \right)\]
• B. \[\left( 0,\frac{11}{8} \right)\]
• C. \[\left( 2,\frac{11}{18} \right)\]
• D. None of these