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A light ray is incident along the line 7x - y - 11 = 0 and reflects off a plane mirror placed along the line x - y + 1 = 0 . If A is the area of the triangle formed by the reflected ray and the coordinate axes, then the value of 14A is equal to

Correct answer

361

Step-by-step solution

Let the incident ray be L₁: 7x - y - 11 = 0 and the mirror be L₂: x - y + 1 = 0 . First, we find the point of incidence by solving the equations of L₁ and L₂ . Subtracting the two equations gives 6x - 12 = 0 x = 2 . Substituting x = 2 into L₂ gives 2 - y + 1 = 0 y = 3 . So, the point of incidence is (2, 3) . The slope of the incident ray is m₁ = 7 and the slope of the mirror is m = 1 . Let the slope of the reflected ray be m₂ . By the laws of reflection, the angle between the incident ray and the mirror is equal to

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