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Let $L$ be a line passing through point $P (1, 2)$ such that its intercepted segment between the Co – ordinate axes is bisected at $P$ . If $L_{1}$ is the line perpendicular to L and passing through the point $(- 2, 1)$ then the point of intersection of $L$ and $L_{1}$ is

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$(\frac{3}{5}, \frac{23}{10})$

$(\frac{4}{5}, \frac{12}{5})$

$(\frac{11}{20}, \frac{29}{10})$

$(\frac{3}{10}, \frac{17}{5})$

answer is B.

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Detailed Solution

Equation of L is $\frac{x}{2} + \frac{y}{4} = 1$

$2 x + y - 4 = 0 (1)$

Equation of $L_{1}$ is y – 1 = $\frac{1}{2} (x + 2)$

$\begin{array}{l} 2 y - 2 = x + 2 \\ x - 2 y + 4 = 0 (2) \end{array}$

Solving 1 & 2 $(\frac{4}{5}, \frac{12}{5})$

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