five students wearing shirts with SAVE ENVIRONMENT are standing on a bench represented by equation 3x+4y+16=0,spotlight is placed at the point (-1,3) what is the distance of spotlight from the bench?what value is indicated by this message?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Line} \mathrm{represented} \mathrm{by} \mathrm{bench} \mathrm{is} 3\mathrm{x}+4\mathrm{y}+16=0 \mathrm{and} \mathrm{spotlight} \mathrm{is} \mathrm{at} \left(-1,3\right) \\ \mathrm{Required} \mathrm{distance} \\ =\mathrm{Perpendicualr} \mathrm{distance} \mathrm{of} \mathrm{point} \left(-1,3\right) \mathrm{from} 3\mathrm{x}+4\mathrm{y}+16=0 \\ =\frac{\left|3\times \left(-1\right)+4\times 3+16\right|}{\sqrt{9+16}} \\ =\frac{\left|-3+12+16\right|}{\sqrt{9+16}} \\ =\frac{\left|25\right|}{\sqrt{25}} \\ =\frac{25}{5} \\ =5 \left[\mathrm{Answer}\right] \end{gathered}$$

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