Question

Three lines $x+2y-7=0,x+2y+3=0$ and $2x-y+4=0$ form $3$ sides of two squares then equation of remaining side of these squares is

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

Answer 1

The correct option is D $2x-y+14=0$

From given lines, we get $x+2y-7=0$ and $x+2y+3=0$ are parallel to each other at a distance of $\frac{10}{\sqrt{5}}$.
And third line is $2x-y+4=0$,

$\therefore$ fourth line should be parallel to third line and at distance $\frac{10}{\sqrt{5}}$,
Let $2x-y+a=0$ be fourth line

Then distance $a-4=10⟹a=14$,
$\therefore$ fourth line is $2x-y+14=0$.