Question

Three lines $x+2y+3=0,x+2y-7=0$ and $2x-y-4=0$ form the three sides of two squares. The equation to the fourth side of each square is

• A. $2x-y+14=0$ and $2x-y+6=0$
• B. $2x-y+14=0$ and $2x-y-6=0$
• C. $2x-y-14=0$ and $2x-y-6=0$
• D. $2x-y-14=0$ and $2x-y+6=0$

Answer 1

Answer: (D)

$2x-y-14=0$ and $2x-y+6=0$

$\begin{array}{c}Lettheequationbefourthsidebe2x-y+c=0\\ \frac{3+7}{\sqrt{5}}=\frac{\left|c+4\right|}{\sqrt{5}}\\ \left|c+4\right|=10\\ \Rightarrow c=6,-14\\ 2x-y+6=0\\ 2x-y-14=0\\ OptionDiscorrectanswer.\end{array}$