Chapter 4.1, Problem 71SPR

To determine

The distance between two parallel lines.

Answer to Problem 71SPR

  $2\sqrt{5}\text{ units}$

Explanation of Solution

Given:

The given lines are:

  $\begin{array}{l}y=2x+3\\ y=2x-7\end{array}$

Calculation:

The equation of the line perpendicular to both the lines will be:

Slope = -1/2 and point = (0, 7).

Therefore,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-7\right)=-\frac{1}{2}\left(x-\left(0\right)\right)\\ y=-\frac{1}{2}x+7\end{array}$

The graph of the lines can be drawn as:

The distance between two parallel lines will be:

  $\begin{array}{l}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(0-\left(-4\right)\right)}^2+{\left(-7-\left(-5\right)\right)}^2}\\ =\sqrt{20}\\ =2\sqrt{5}\text{ units}\end{array}$