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A=(2,5),B=(4,-11) and the locus of `C’ is 9x+7y+4=0 then the locus of the centroid of $∆ A B C$ is

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$27 x + 21 y - 8 = 0$

$3 x + 4 y - 2 = 0$

$24 x + 22 y - 6 = 0$

$5 x + 3 y - 7 = 0$

answer is A.

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Detailed Solution

$A (2, 5), B (4, - 11), C (x, y)$

$G = (\frac{2 + 4 + x}{3}, \frac{5 - 11 + y}{3}), (h, k) = (\frac{6 + x}{3}, \frac{- 6 + y}{3})$

$3 h - 6 = x, 3 k + 6 = y$

$(x, y) lines on 9 x + 7 y + 4 = 0$

$9 (3 h - 6) + 7 (3 k + 6) + 4 = 0$

$Locus is 27 x + 21 y - 8 = 0$

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