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Q.

A light beam, emanating from the point (3,10) reflects from the straight line $2 x + y − 6 = 0$ and, then passes through the point (7,2).If the equation of the reflected beam is written as $x + m y − 13 = 0$ , then m is______

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answer is 3.

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Detailed Solution

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Let $A (3, 10), B (7, 2)$ Let images of A and B about the line $2 x + y − 6 = 0$ are
$A^{1} (α, β) and B^{1} (γ, δ)$ respectively. Then $α = − 5, β = 6 ⇒ A 1 = (− 5, 6)$
Equation of reflected ray $A^{'} B is$
$x + 3 y - 13 = 0 \Rightarrow m = 3$

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