Chapter 3.3, Problem 28PPS

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 28PPS

The lines are parallel.

Explanation of Solution

Given information:

  $A(1,5),B(4,4),C(9,-10),D(-6,-5)$

Formulaused:

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

Where, $m$ is slope and $y_2^{}-y_1^{}$ are difference in y coordinates and $x_2^{}-x_1^{}$ difference in x coordinates.

Calculation:

For AB ,

  $x_1^{}=1,y_1^{}=5$

  $x_2^{}=4,y_2^{}=4$

Substituting value,

Slope of line is, $m=\frac{4-5}{4-1}$

Solving,

$m=\frac{-1}{3}$

Slope for AB is $\frac{-1}{3}$ .

For CD ,

  $x_1^{}=9,y_1^{}=-10$

  $x_2^{}=-6,y_2^{}=-5$

Substituting value,

Slope of line is, $m=\frac{-5-(-10)}{-6-9}$

Solving,

$m=\frac{-5+10}{-15}$

Slope is $\frac{-1}{3}$ .

Now, line is parallel as slope are equal.

Graph:

Interpretation:

Green line represents AB and blue line represents CD .

The lines are parallel.