Question

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

• A. $2x-y+6=0$
• B. $2x-y+8=0$
• C. $2x-y-10=0$
• D. $2x-y-14=0$

Answer 1

The correct option is A $2x-y+6=0$

Here $x+2y+3=0$ and $x+2y-7=0$ are parallel lines

Let fourth line equation be $2x-y+c=0$ as it is

parallel is $2x-y-4=0$

The distance between the parallel lines is equal

$\therefore \frac{|3-(-7\left)\right|}{\sqrt{1^2+2^2}}=\frac{|c-4|}{\sqrt{2^2+(-1{)}^2}}$

$\therefore \frac{10}{\sqrt{5}}=\frac{|c-4|}{\sqrt{5}}\Rightarrow 10=|c-4|$

$\therefore c-4=10$ or $c-4=-10$

$\therefore c=14$ or $c=-6$

So, fourth equation is $2x-y+14=0$ or $2x-y-6=0$