Chapter 1.4, Problem 81E

To determine

To check if the lines are parallel, perpendicular, or neither

Answer to Problem 81E

Neither

Explanation of Solution

Given:

  $\begin{array}{l}{L}_1:(-2,-2),(2,10)\\ L_2:(-1,3),(3,9)\end{array}$

Formula:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Concept:

Parallel lines:

The slopes of both the lines are equal

Perpendicular lines:

The slopes of both the lines are negative reciprocal of each other.

Calculation:

For line $L_1$ ,

  $(x_1,y_1),(x_2,y_2)=(-2,-2),(2,10)$

Slope of line $L_1$ :

  $\begin{array}{c}{m}_1=\frac{10-(-2)}{2-(-2)}\\ =\frac{10+2}{4}\\ =\frac{12}{4}\\ =3\end{array}$

For line $L_2$ ,

  $(x_1,y_1),(x_2,y_2)=(-1,3),(3,9)$

Slope of line $L_2$ :

  $\begin{array}{c}{m}_1=\frac{9-3}{3-(-1)}\\ =\frac{6}{4}\\ =\frac{3}{2}\end{array}$

The slopes of both the lines are not equal.

So, the lines are not parallel.

Also, 3 is not the negative reciprocal of $\frac{3}{2}$ .

So, the lines are not perpendicular.

Conclusion:

Therefore, the lines are neither parallel nor perpendicular.