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  • A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on -axis. I

A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on x-axis. If the reflected ray passes through the point (6, 4), then the coordinates of P are

 

Option: 1

\left(\frac{26}{7}, 0\right)


Option: 2

\left(\frac{-26}{7}, 0\right)


Option: 3

\left(\frac{13}{7}, 0\right)


Option: 4

\left(\frac{-13}{7}, 0\right)


Answers (1)

best_answer

Method 1.
Let the reflected ray makes an angle \theta with + ve direction of x-axis, then the incident ray makes angle (\pi-\theta)  with positive direction of \mathrm{x}-axis.

Now, the slope of the incident ray



Slope of the reflected ray is \mathrm{=\frac{4-0}{6-\alpha}=\tan}

\mathrm{\Rightarrow \frac{4-0}{6-\alpha}\quad \ldots(2)}

from (1) and (2) we get
\mathrm{\alpha=\frac{26}{7}}
 

Method 2.
Take the image of P(2, 3) about the x-axis, which is \mathrm{P^{\prime}}. Now \mathrm{P^{\prime}QR} will be collinear.
Hence first find the equation of line \mathrm{P^{\prime} Q} and then find the point of intersection of \mathrm{P^{\prime} Q} with the x-axis to get the required point. \mathrm{P^{\prime} \equiv(2, -3)},  equation of \mathrm{P^{\prime} Q} is \mathrm{7 x-4 y=26}.

Hence the required point is \mathrm{\left(\frac{26}{7}, 0\right)}


Hence (A) is the correct answer.

Posted by

sudhir.kumar

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