Question

If the lines $x+2y+3=0,x+2y-7=0$ and $2x-y-4=0$ are the sides of a square, then equation of the remaining sides 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

Answer: (A), (D)

The correct options are
A $2x-y+6=0$
D $2x-y-14=0$

Given eq of lines of sides of square are

$x+2y+3=0$

$x+2y-7=0$ and $2x-y-4=0$

Here since the first two lines are parallel as they have same slope and distance between them is $|3-(-x)|$ i.e, 10 hence the fourth $E{q}^n$ of the line to form a square would be a line with slope 2 and at a distance 10 from the third line

ie, $2x-y-4\pm 10=0$

Or, $2x-y+6=0,2x-y-14=0$