Chapter 4, Problem 14CR

To determine

To calculate:

Lines whether they are parallel or perpendicular from the given graph.

Answer to Problem 14CR

Line $c$ and line $d$ are parallel to each other.

Explanation of Solution

Given information:

  

Calculation:

From the given graph, it is observed that,

Line $a$ passes through $\left(2,2\right),\left(-2,3\right)$ , line $b$ passes through $\left(3,-2\right)\left(-3,0\right)$ , line $c$ passes through $\left(2,4\right)\left(0,-2\right)$ , line $d$ passes through $\left(0,6\right)\left(-2,0\right)$ .

Now, calculate slope of each line,

Slopes for line $a$ ,

  $\begin{array}{l}=\frac{3-2}{-2-2}\\ =\frac{1}{-4}\\ =-0.25\end{array}$

Slopes for line $b$ ,

  $\begin{array}{l}=\frac{0-\left(-2\right)}{\left(-3\right)-3}\\ =\frac{2}{-6}\\ =-0.33\end{array}$

Slopes for line $c$ ,

  $\begin{array}{l}=\frac{\left(-2\right)-4}{0-2}\\ =\frac{-6}{-2}\\ =3\end{array}$

Slopes for line $d$ ,

  $\begin{array}{l}=\frac{0-6}{\left(-2\right)-0}\\ =\frac{-6}{-2}\\ =3\end{array}$

From the determined slopes, it is observed that, line $c$ and $d$ are parallel because they share the same slope. i.e. $3$ .

Thus, line $c\Vert d$ .