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The line segment joining the points $(3, 4)$ and $(k, 2)$ is divided by the line $2 x + 3 y + 5 = 0$ in the ratio 2:3 then $k =$

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$\frac{- 91}{4}$

$- 91$

answer is A.

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Detailed Solution

Let L = 2x + 3y + 5 = 0 and the points be A(3,4) B(k,2)

Ratio = $\frac{- L_{11}}{L_{22}} = \frac{- (23)}{2 k + 11} = \frac{2}{3}$ (given)

$\Rightarrow k = \frac{- 91}{4}$

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