Explanation

(c)
The separate equation of pair of straight lines of ${12x}^{2} - 20xy + 7y^{2} = 0$ are $6x - 7y = 0$ and $2x - y = 0$
Thus, equation of sides of triangle are
$6x - 7y = 0$ …(i)
$2x - y = 0$ …(ii)
$and\ 2x - 3y + 4 = 0$ …(iii)
On solving these equations, we get the vertices of a triangle $A(0,\ 0);B(1,2)and\ C(7,6)$
$\therefore$ Centroid of triangle is
$\left( \frac{0 + 1 + 7}{3},\frac{0 + 2 + 6}{3} \right) = \left( \frac{8}{3},\frac{8}{3} \right)$