Chapter 3, Problem 16PT

To determine

The distance between the given parallel lines.

Answer to Problem 16PT

The distance between the parallel lines is 4.

Explanation of Solution

Given:

Lines:

  $\begin{array}{l}y=x-11\\ y=x-7\end{array}$

Solution:

When the slope of parallel lines are equal, the distance between them is calculated by using given formula below:

  $d=\left|c_1-c_2\right|$

So,

From the given description,

  $\begin{array}{l}y=x-11\\ y=x-7\end{array}$

The slope of both lines is equal,

i.e.,

  $m_1=m_2=1$

And,

  $\begin{array}{l}{c}_1=-11\\ c_2=-7\end{array}$

Therefore,

Distance between parallel lines,

  $\begin{array}{l}d=\left|-11-\left(-7\right)\right|\\ d=\left|-11+7\right|\\ d=\left|-4\right|\\ d=4\end{array}$

So, the distance between the parallel lines is 4.