Chapter 3.3, Problem 30PPS

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 30PPS

The lines are intersecting. So neither parallel nor perpendicular

Explanation of Solution

Given information:

  $A(4,2),B(-3,1),C(6,0),D(-10,8)$

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 ,

  $x_1^{}=4,y_1^{}=2$

  $x_2^{}=-3,y_2^{}=1$

Substituting value,

Slope of line is, $m=\frac{1-2}{-3-4}$

Solving,

$m=\frac{-1}{7}$

Slope for AB is $m=\frac{-1}{7}$ .

For CD ,

  $x_1^{}=6,y_1^{}=0$

  $x_2^{}=-10,y_2^{}=8$

Substituting value,

Slope of line is, $m=\frac{8-0}{-10-6}$

Solving,

$m=\frac{8}{-16}$

Slope is $\frac{-1}{2}$ .

Now, lines are not parallel as slope are not equal.

Product of slopes= $\frac{-1}{7}\times \frac{-1}{2}\ne -1$

Lines are not perpendicular.

Graph:

Interpretation:

Green line represents AB and blue line represents CD .

The lines are intersecting. So neither parallel nor perpendicular.