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Q.

The equation of line bisecting the join of $(1, - 2)$ and $(2, - 5)$ having its intercepts on $x -$ axis and $y -$ axis in the ratio of $2 : 3$ is

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a

$3 x + 2 y + \frac{5}{2} = 0$

b

$3 x + 4 y + \frac{5}{2} = 0$

c

$4 x + 3 y + \frac{5}{2} = 0$

d

$3 x - 4 y + \frac{5}{2} = 0$

answer is C.

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Detailed Solution

mid-point of $(1, - 2)$ and $(2, - 5)$ is $(\frac{3}{2}, \frac{- 7}{2})$
Req d equation is $\frac{x}{2 a} + \frac{y}{3 a} = 1$
$\frac{3}{4 a} - \frac{7}{6 a} = 1 \frac{9 - 14}{12 a} = 1 \Rightarrow a = \frac{- 5}{12} ∴ \frac{- 6 x}{5} - \frac{4 y}{5} = 1 \Rightarrow - 6 x - 4 y = 5$

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