A point P moves on the line 2x - 3y + 4 = 0. If Q(l, 4) and R(3, -2) are fixed points, then the locus

of the centroid of $\mathrm{△}PQR$ is a line

Let the coordinates of the centroid G of the $\mathrm{△}PQR$ are (h, k) and coordinates of P are (m, n).

$\therefore h=\frac{m+1+3}{3}$ and $k=\frac{n+4-2}{3}$

$\Rightarrow m=3h-4$ and $n=3k-2$

Now, P(m, n) lies on the line

$\begin{array}{l}2x-3y+4=0\therefore 2m-3n+4=0\\ \Rightarrow 2(3h-4)-3(3k-2)+4=0\\ \Rightarrow 6h-8-9k+6+4=0\Rightarrow 6h-9k+2=0\end{array}$

$\therefore$ Locus of (h, k) is 6x - 9y + 2 = 0

 So, slope of the above line is 2/3.