# Equation of line in Straight lines

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# A ray of light along $\mathrm{x}+\sqrt{3}\mathrm{y}=\sqrt{3}$ reflected on reaching  x-axis the equation of the reflected ray is y = mx + c then $\left|\frac{\mathrm{c}}{\mathrm{m}}\right|=$

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Solution

## To get the reflected ray equation, find the equation of the line passing through the point of intersection of incident ray,   x-axis and the image of any point on the incident ray with respect to the  x- axis The line $\mathrm{x}+\sqrt{3}\mathrm{y}=\sqrt{3}$ meets   x-axis at $A\left(\sqrt{3},0\right)$A point on the line $\mathrm{x}+\sqrt{3}\mathrm{y}=\sqrt{3}$ is  $B\left(0,1\right)$The image of  B with respect to  x-axis is  ${\mathrm{B}}^{\text{'}}\left(0,-1\right)$The equation of the reflected ray is the line passing through the point  $\mathrm{A}\left(\sqrt{3},0\right)$ and ${\mathrm{B}}^{\text{'}}\left(0,-1\right)$$\mathrm{y}+1=\frac{0+1}{\sqrt{3}-0}\left(\mathrm{x}-0\right)$Therefore, the equation of the reflected ray is  $\overline{)\sqrt{3}y=x-\sqrt{3}}$

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