JEE Mains · Maths · STD 11 - 9. straight line
A ray of light passing through the point \(P (2,3)\) reflects on the \(x-\)axis at point \(A\) and the reflected ray passes through the point \(Q(5,4)\). Let \(R\) be the point that divides the line segment \(AQ\) internally into the ratio \(2: 1\). Let the co-ordinates of the foot of the perpendicular \(M\) from \(R\) on the bisector of the angle \(PAQ\) be \((\alpha, \beta)\). Then, the value of \(7 \alpha+3 \beta\) is equal to.......
- A \(31\)
- B \(91\)
- C \(310\)
- D \(312\)
Answer & Solution
Correct Answer
(A) \(31\)
Step-by-step Solution
Detailed explanation
By observation we see that \(A (\alpha, 0)\). And \(\beta= y\)-cordinate of \(R\) \(=\frac{2 \times 4+1 \times 0}{2+1}=\frac{8}{3} \ldots(1)\) Now \(P'\) is image of \(P\) in \(y =0\) which will be \(P ^{\prime}(2,-3)\) Equation of \(P ^{\prime} Q\) is…
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