Question

Find the distance between $x+y+1=0$ and $2x+2y+5=0$.

Answer 1

The given equations can be written as

$x+y+1=0$.......(1) and $x+y+\frac{5}{2}=0$......(2).

It is clear that the given two straight lines are on the same side of the origin.

Then the distance between the two straight lines is

$=\left|\frac{\frac{5}{2}-1}{\sqrt{1^2+1^2}}\right|=\frac{3}{2\sqrt{2}}$ units.