Chapter 3.6, Problem 3ACYP

To determine

To Find: The distance between each pair of parallel lines.

Answer to Problem 3ACYP

  $\frac{11}{\sqrt{10}}$

Explanation of Solution

Given:

  

Two parallel lines $r$ and $s$ :

  $y=-3x-5,y=-3x+6$

Formula Used:

Distance between two parallel lines: $y=mx+c_1,y=mx+c_2$ is given as:

  $D=\frac{|c_1-c_2|}{\sqrt{1+m^2}}$

Comparing the given equations with formula equations:

  $\begin{array}{l}m=-3\\ c_1=-5\\ c_2=6\end{array}$

Distance between the lines is:

  $D=\frac{|-5-6|}{\sqrt{1+{(-3)}^2}}=\frac{11}{\sqrt{10}}$