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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 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

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 x-axis.
Now, the slope of the incident ray
\begin{array}{ll} & =\frac{0-3}{\alpha-2}=\tan (\pi-\theta) \\ \Rightarrow \quad & \tan (\pi-\theta)=\frac{0-3}{\alpha-2} \quad \quad \ldots (i) \end{array}

Slope of the reflected ray is


\begin{array}{ll} & \frac{4-0}{6-\alpha}=\tan \theta \\ \Rightarrow \quad & \tan \theta=\frac{4-0}{6-\alpha}\quad \quad \ldots (ii) \end{array}

From Eqs. (i) and (ii), we get
\alpha=\frac{26}{7}
 

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