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  •  A ray of light coming from the point gets is reflected at a point <img alt="\mathrm{A}" src="https://entr

 A ray of light coming from the point (1,2) gets is reflected at a point \mathrm{A} on the \mathrm{x}-axis and then passes through the point (5,3), then the co-ordinates of the point  \mathrm{A} is

Option: 1

\left(\frac{13}{5}, 0\right)


Option: 2

\left(\frac{5}{13}, 0\right)


Option: 3

(-7,0)


Option: 4

 none of these


Answers (1)

best_answer

Let the co-ordinates of \mathrm{A} be \mathrm{(a, 0)}

Then the slope of the reflected ray is \mathrm{\frac{3-0}{5-a}=\tan \theta\: (say) \: \cdots(i)}

Then the slope of the incident ray \mathrm{=\frac{2-0}{1-a}=\tan (\pi-\theta) \cdots(ii)}

\mathrm{From \, (i) \: and\: (ii),\tan \theta+\tan (\pi-\theta)=0}

\mathrm{\Rightarrow \quad \frac{3}{5-a}+\frac{2}{1-a}=0 \quad \Rightarrow \quad 3-3 a+10-2 a=0 \Rightarrow a=\frac{13}{5}}

Thus, the co-ordinates of \mathrm{A} are \mathrm{\left(\frac{13}{5}, 0\right)}

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Riya

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