Question

Line ℓ1 has the equation y=

-
x+5 and line ℓ2 has the equation x+y=
-
1. Find the distance between ℓ1 and ℓ2.

Answer 1

`d = (6)/(√(2) )` units

Explanation:

The two lines are
`y + x - 5 = 0` and
`y + x + 1 = 0`

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

`a x + b y + c 1 = 0`

`a x + b y + c 2 = 0`

the distance between them can be expressed as ( modulus of any answer obtained, as the distance can not be a negative quantity.)

`d = \frac{( c2 - c1)}{\sqrt{a^(2)+b^(2)}}`

According to lines here,

`y + x - 5 = 0`

`y + x + 1 = 0`

`d = \frac{( 1 - (-5))}{\sqrt{1^(2)+1^(2)}}`

`d = (6)/(√(2) )`

The distance between these two line is
`d = (6)/(√(2) )` units