JEE Mains · Maths · STD 11 - 9. straight line
From the point \((-1, -1)\), two rays are sent making angles of \(45°\) with the line \(x + y = 0\). These rays get reflected from the mirror \(x + 2y = 1\). If the equations of the reflected rays are \(ax + by = 9\) and \(cx + dy = 7\), \(a, b, c, d \in \mathbf{Z}\), then the value of \(ad + bc\) is _______.
- A 5
- B 7
- C 9
- D 11
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
The given line is \(x + y = 0\), which has a slope of \(m_1 = -1\). Let the slope of an incident ray be \(m\). Since it makes an angle of \(45^{\circ}\) with the line \(x + y = 0\), we have: \(\left| \dfrac{m - (-1)}{1 + m(-1)} \right| = \tan 45^{\circ} = 1\)…
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