A(2,3) and B(3,-5) are two vertices of triang | vedclass

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(A) Let the coordinates of vertex $C$ be $(h,k)$.The centroid $G(x,y)$ of $	riangle ABC$ with vertices $A(2,3)$,$B(3,-5)$,and $C(h,k)$ is given by:$x

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$2x+y+2=0$

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(A) Let the coordinates of vertex $C$ be $(h,k)$.The centroid $G(x,y)$ of $	riangle ABC$ with vertices $A(2,3)$,$B(3,-5)$,and $C(h,k)$ is given by:$x = \frac{2+3+h}{3} = \frac{5+h}{3} \implies h = 3x-5$$y = \frac{3-5+k}{3} = \frac{k-2}{3} \implies k = 3y+2$Since the centroid $G(x,y)$ lies on the line $2x+y-2=0$,we substitute $x = \frac{h+5}{3}$ and $y = \frac{k-2}{3}$ into the equation:$2(\frac{h+5}{3}) + (\frac{k-2}{3}) - 2 = 0$Multiply by $3$:$2(h+5) + (k-2) - 6 = 0$$2h + 10 + k - 2 - 6 = 0$$2h + k + 2 = 0$Replacing $(h,k)$ with $(x,y)$,the locus of $C$ is $2x+y+2=0$.

$A(2,3)$ and $B(3,-5)$ are two vertices of $\triangle ABC$. If the centroid of the $\triangle ABC$ moves on the line $2x+y-2=0$,then the locus of $C$ is

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