Chapter 3.3, Problem 5CYU

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 5CYU

The lines are perpendicular.

Explanation of Solution

Given information:

  $W(2,4),X(4,5),Y(4,1),Z(8,-7)$

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 ,

  $x_1^{}=2,y_1^{}=4$

  $x_2^{}=4,y_2^{}=5$

Substituting value,

Slope of line is, $m=\frac{5-4}{4-2}$

Solving,

$m=\frac{1}{2}$

Slope for WX is $\frac{1}{2}$ .

For YZ ,

  $x_1^{}=4,y_1^{}=1$

  $x_2^{}=8,y_2^{}=-7$

Substituting value,

Slope of line is, $m=\frac{-7-1}{8-4}$

Solving,

$m=\frac{-8}{4}$

Slope is $-2$ .

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

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

The line is perpendicular.