Let $A(2,3)$ and $B(-2,3)$ be vertices of a triangle ABC. If the centriod of this triangle moves on the line $2x+3y=1$ then the locus of the vertex C is the line .

Question

$\begin{array}{1 1}(A)\;3x-2y=3\\(B)\;2x-3y=7\\(C)\;3x+2y=5\\(D)\;2x+3y=9\end{array}$