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)

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}} $