Chapter 1.4, Problem 82E

To determine

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

Answer to Problem 82E

Neither

Explanation of Solution

Given:

  $\begin{array}{l}{L}_1:(-1,-7),(4,3)\\ L_2:(1,5),(-2,-7)\end{array}$

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 $L_1$ ,

  $(x_1,y_1),(x_2,y_2)=(-1,-7),(4,3)$

Slope of line $L_1$ :

  $\begin{array}{c}{m}_1=\frac{3-(-7)}{4-(-1)}\\ =\frac{10}{5}\\ =2\end{array}$

For line $L_2$ ,

  $(x_1,y_1),(x_2,y_2)=(1,5),(-2,-7)$

Slope of line $L_2$ :

  $\begin{array}{c}{m}_1=\frac{-7-5}{-2-1}\\ =\frac{-12}{-3}\\ =6\end{array}$

The slopes of both the lines are not equal.

So, the lines are not parallel.

Also, 2 is not the negative reciprocal of 6.

So, the lines are not perpendicular.

Conclusion:

Therefore, the lines are neither parallel nor perpendicular.