Chapter 3.3, Problem 6CYU

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 6CYU

The lines are neither parallel nor perpendicular.

Explanation of Solution

Given information:

  $W(1,3),X(-2,-5),Y(-6,-2),Z(8,3)$

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 WX ,

  $x_1^{}=1,y_1^{}=3$

  $x_2^{}=-2,y_2^{}=-5$

Substituting value,

Slope of line is, $m=\frac{-5-3}{-2-1}$

Solving,

$m=\frac{-8}{-3}$

Slope for WX is $\frac{8}{3}$ .

For YZ ,

  $x_1^{}=-6,y_1^{}=-2$

  $x_2^{}=8,y_2^{}=3$

Substituting value,

Slope of line is, $m=\frac{-2-3}{8-(-6)}$

Solving,

$m=\frac{-5}{14}$

Slope is $-2$ .

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

Product of slopes=

  $\frac{-5}{4}\times \frac{8}{3}\ne -1$

The line is not perpendicular.