Chapter 3.6, Problem 22PPS

To determine

To find distance between parallel lines.

  $x=3$

  $x=7$

Answer to Problem 22PPS

  $d=1units$

Explanation of Solution

Given information:

Parallel lines

  $x=3$

  $x=7$

Formula used:

Distance from point to line

  $d=\frac{|c_1-c_2|}{\sqrt{A^2+B^2}}$

Where

  $c_1$ and $c_2$ are intercept of lines.

Line 1

  $Ax+By+c_1=\mathrm{0.............}(1)$

Line 2

  $Ax+By+c_2=\mathrm{0............}(2)$

  $A$ and $B$ are the coefficient.

Calculation:

Parallel lines

  $x=3$

  $x=7$

Rewrite equations

  $x-3=0$

  $x-7=0$

Here

  $A=1$

  $B=0$

  $c_1=-3$

  $c_2=-7$

Using distance formula

Substitute value of $A$ , $B$ , $c_1$ and $c_2$

  $d=\frac{|-3-(-4)|}{\sqrt{1^2+0^2}}$

On solving

  $d=\frac{|-3+4|}{\sqrt{1}}$

On solving

  $d=\frac{\left|1\right|}{1}$

On solving

  $d=1units$

Hence, distance between parallel lines is $1units$