Chapter 3.3, Problem 3ACYP

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 3ACYP

The lines are neither parallel nor perpendicular

Explanation of Solution

Given information:

  $A(14,13),B(-11,0),C(-3,7),D(-4,-5)$

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,

  $x_1^{}=14,y_1^{}=13$

  $x_2^{}=-11,y_2^{}=0$

Substituting value,

Slope of line is, $m=\frac{-11-14}{0-13}$

Solving,

$m=\frac{-25}{-13}$

Slope for AB is $\frac{-25}{-13}$

For CD,

  $x_1^{}=-3,y_1^{}=7$

  $x_2^{}=-4,y_2^{}=-5$

Substituting value,

Slope of line is, $m=\frac{-4-(-3)}{-5-7}$

Solving,

$m=\frac{-1}{-12}$

Slope is $\frac{1}{12}$ .

Now, line is not parallel as slope is not equal.

Product of slopes= $\frac{25}{13}\times \frac{1}{12}\ne -1$

The line is not perpendicular.