Chapter 3.6, Problem 7CYU

To determine

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

Answer to Problem 7CYU

  $2\sqrt{5}$

Explanation of Solution

Given:

Two parallel lines:

  $y=-2x+4,y=-2x+14$

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:

  $\begin{array}{l}m=-2\\ c_1=4\\ c_2=14\end{array}$

Distance between the lines is:

  $D=\frac{|4-14|}{\sqrt{1+{(-2)}^2}}=\frac{10}{\sqrt{5}}=2\sqrt{5}$