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If the line $2x - 3y + 4 = 0$ divides the line segment joining the points A(-2, 3) and B(3, -2) in the ratio m : n then the point which divides AB in the ratio – 4 m : 3n is

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(-17, 18)

$(\frac{-59}{7}, \frac{66}{7})$

(- 5, 6)

$(\frac{-5}{7}, \frac{12}{7})$

answer is A.

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Detailed Solution

$L \equiv 2x - 3y + 4 = 0$

$L_{11} = L (-2, 3) = - 9$

$L_{22} = 2 (3, -2) = 16$

Ratio = - L₁₁ : L₂₂ = 9 : 16

$\frac{-4m}{3n} = \frac{-4}{3} (\frac{9}{16}) = \frac{-3}{4}$

Apply section formula.

$Reqpt = (\frac{3 (3) -4 (-2)}{3-4}, \frac{3 (-2) - 4 (3)}{3-4})$

= (-17, 18)

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