Let P(2, -3) and Q(-2, 1) be the vertices of | vedclass

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(A) Let the coordinates of vertex $R$ be $(h, k)$.The centroid of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by $\le

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$2x + 3y = 9$

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(A) Let the coordinates of vertex $R$ be $(h, k)$.The centroid of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by $\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$.Substituting the given vertices $P(2, -3), Q(-2, 1),$ and $R(h, k)$, the centroid is $\left(\frac{2 - 2 + h}{3}, \frac{-3 + 1 + k}{3}\right) = \left(\frac{h}{3}, \frac{k - 2}{3}\right)$.Since the centroid lies on the line $2x + 3y = 1$, the coordinates must satisfy the equation:$2\left(\frac{h}{3}\right) + 3\left(\frac{k - 2}{3}\right) = 1$Multiplying by $3$, we get:$2h + 3(k - 2) = 3$$2h + 3k - 6 = 3$$2h + 3k = 9$Replacing $(h, k)$ with $(x, y)$, the locus of $R$ is $2x + 3y = 9$.

Let $P(2, -3)$ and $Q(-2, 1)$ be the vertices of the $\Delta PQR$. If the centroid of $\Delta PQR$ lies on the line $2x + 3y = 1$, then the locus of $R$ is

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