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  • The perpendicular distance between <img alt="\mathrm{3 x+4 y-5=0\, \: and \,\: 6 x+8 y-45=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x&plus;4%20y-5%3D0%5C%2C%20%5C

The perpendicular distance between \mathrm{3 x+4 y-5=0\, \: and \,\: 6 x+8 y-45=0} is:

Option: 1

2


Option: 2

3.5


Option: 3

4


Option: 4

4.5


Answers (1)

best_answer

By putting \mathrm{x=0} and \mathrm{y=0} in the equation we get negative values so the roots lie on one side of the two lines.

The length of perpendicular from \mathrm{(0,0) \: to \: 3 x+4 y-5=0} is
\mathrm{=\left|\frac{-5}{\sqrt{3^{2}+4^{2}}}\right|=\left|\frac{-5}{5}\right|=|-1|=1}

The length of perpendicular from \mathrm{(0,0)\: to \: 6 x+8 y-45=0} is
\mathrm{=\left|\frac{-45}{\sqrt{6^{2}+8^{2}}}\right|=\left|\frac{-45}{8}\right|=\left|\frac{-9}{2}\right|=\frac{9}{2}}

Distance between the lines
\mathrm{=\frac{9}{2}-1=\frac{7}{2}=3.5}.

Hence (B) is the correct answer.

Posted by

vishal kumar

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