If A is (2, 5),B is (4, -11) and C lies on 9x | vedclass

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(C) Let the centroid of $\Delta ABC$ be $G(h, k)$.Given $A = (2, 5)$ and $B = (4, -11)$. Let $C = (x, y)$.The coordinates of the centroid are given by

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$9x + 7y + 4 = 0$

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(C) Let the centroid of $\Delta ABC$ be $G(h, k)$.Given $A = (2, 5)$ and $B = (4, -11)$. Let $C = (x, y)$.The coordinates of the centroid are given by $h = \frac{2 + 4 + x}{3}$ and $k = \frac{5 - 11 + y}{3}$.From these,we get $x = 3h - 6$ and $y = 3k + 6$.Since $C(x, y)$ lies on the line $9x + 7y + 4 = 0$,we substitute the values of $x$ and $y$:$9(3h - 6) + 7(3k + 6) + 4 = 0$$27h - 54 + 21k + 42 + 4 = 0$$27h + 21k - 8 = 0$Replacing $(h, k)$ with $(x, y)$,the locus is $27x + 21y - 8 = 0$.Dividing by $3$,we get $9x + 7y - \frac{8}{3} = 0$.This line is parallel to $9x + 7y + 4 = 0$.

If $A$ is $(2, 5)$,$B$ is $(4, -11)$ and $C$ lies on $9x + 7y + 4 = 0$,then the locus of the centroid of the $\Delta ABC$ is a straight line parallel to the straight line:

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