If A(2,-3) and B(-2,1) are two vertices of a | vedclass

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(C) Let the vertices of the triangle be $A(2, -3)$,$B(-2, 1)$,and $C(x_0, y_0)$.Since the third vertex $C$ lies on the line $2x + 3y = 9$,we have $2x_

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$2x + 3y = 1$

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(C) Let the vertices of the triangle be $A(2, -3)$,$B(-2, 1)$,and $C(x_0, y_0)$.Since the third vertex $C$ lies on the line $2x + 3y = 9$,we have $2x_0 + 3y_0 = 9$.Let the centroid of the triangle be $G(h, k)$.The coordinates of the centroid are given by:$h = \frac{2 - 2 + x_0}{3} = \frac{x_0}{3} \implies x_0 = 3h$$k = \frac{-3 + 1 + y_0}{3} = \frac{y_0 - 2}{3} \implies y_0 = 3k + 2$Substituting $x_0$ and $y_0$ into the equation of the line $2x_0 + 3y_0 = 9$:$2(3h) + 3(3k + 2) = 9$$6h + 9k + 6 = 9$$6h + 9k = 3$Dividing by $3$,we get $2h + 3k = 1$.Replacing $(h, k)$ with $(x, y)$,the locus is $2x + 3y = 1$.

If $A(2,-3)$ and $B(-2,1)$ are two vertices of a triangle and the third vertex moves on the line $2x + 3y = 9$,then the locus of the centroid of the triangle is

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