Question

The distance between the parallel lines $y=x+a,\,\,y=x+b$ is

• A. $\frac{|b-a|}{\sqrt{2}}$
• B. $|a-b|$
• C. $|a+b|$
• D. $\frac{|a+b|}{\sqrt{2}}$

Answer 1

Answer: (A)

$\frac{|b-a|}{\sqrt{2}}$

Answer 2

The distance between two parallel lines
$=\frac{|{{c}_{1}}-{{c}_{2}}|}{\sqrt{{{a}^{2}}+{{b}^{2}}}}$
$\therefore$ Distance $=\frac{|b-a|}{\sqrt{{{1}^{2}}+{{1}^{2}}}}$ $=\frac{|b-a|}{\sqrt{2}}$