Let $A=(2,3)B=(3,-5)$ be two vertices of $\Delta ABC$ such that C is a point on the line $L=3x+4y-5=0.$ Then the locus of the centroid of $\Delta ABC$ is a line parallel to

$$\begin{gathered} h=\frac{2+3+x}{3},k\frac{3-5+y}{3} \\ \begin{array}{l}\Rightarrow x=3h-5\Rightarrow y=3k+2\\ Clieonline3x+4y-5=0\\ 3(3h-5)+4(3k+2)-5=0\\ \Rightarrow 9h-15+12k+8-5=0\\ \Rightarrow 9h+12k-12=0\Rightarrow 3h+4k-4=0\end{array} \end{gathered}$$
Locus of centroid is $3x+4y-4=0$ which is parallel to line L = 0