Answer:
[tex]d = \frac{6}{\sqrt{2} }[/tex] units
Step-by-step explanation:
The two lines are [tex]y + x - 5 = 0[/tex] and [tex]y + x + 1 = 0[/tex]
These two lines are parallel as they have the same slope = -1.
The shortest distance between any two parallel lines,
When the lines are given by
[tex]a x + b y + c 1 = 0[/tex]
[tex]a x + b y + c 2 = 0[/tex]
the distance between them can be expressed as ( modulus of any answer obtained, as the distance can not be a negative quantity.)
[tex]d = \frac{( c2 - c1)}{\sqrt{a^{2}+b^{2}}}[/tex]
According to lines here,
[tex]y + x - 5 = 0[/tex]
[tex]y + x + 1 = 0[/tex]
[tex]d = \frac{( 1 - (-5))}{\sqrt{1^{2}+1^{2}}}[/tex]
[tex]d = \frac{6}{\sqrt{2} }[/tex]
The distance between these two line is [tex]d = \frac{6}{\sqrt{2} }[/tex] units
