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

The lines \mathrm{x+2 y+3=0, x+2 y-7=0 \: and \: 2 x-y-4=0} are the sides of a square. Equation of the remaining side of the square can be -
 

Option: 1

2 \mathrm{x}-\mathrm{y}-14=0


 


Option: 2

\mathrm{2 x-y+8=0}
 


Option: 3

2 \mathrm{x}-\mathrm{y}-10=0
 


Option: 4

2 \mathrm{x}-\mathrm{y}-6=0


Answers (1)

best_answer

Distance between \mathrm{x+2 y+3=0\: and \: x+2 y-7=0 \: is \: \frac{10}{\sqrt{5}}}. Let the remaining side be \mathrm{2 x-y+\lambda=0.}

We have, \mathrm{\frac{|\lambda+4|}{\sqrt{5}}=\frac{10}{\sqrt{5}} \Rightarrow \lambda=5,-14}, thus remaining side is

\mathrm{2 x-y+6=0 \, or \: 2 x-y-14=0}

Hence option 1 is correct.

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