Chapter 3.3, Problem 32PPS

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 32PPS

The lines are perpendicular.

Explanation of Solution

Given information:

  $A(8,4),B(4,3),C(4,-9),D(2,-1)$

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 ,

  $x_1^{}=8,y_1^{}=4$

  $x_2^{}=4,y_2^{}=3$

Substituting value,

Slope of line is, $m=\frac{3-4}{4-8}$

Solving,

$m=\frac{-1}{-4}$

Slope for AB is $\frac{1}{4}$ .

For CD ,

  $x_1^{}=4,y_1^{}=-9$

  $x_2^{}=2,y_2^{}=-1$

Substituting value,

Slope of line is, $m=\frac{-1-(-9)}{-2-4}$

Solving,

$m=\frac{8}{-2}$

Slope is $-4$ .

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

Product of slope= $\frac{1}{4}\times (-4)=-1$

The lines are perpendicular

Graph:

Interpretation:

Green line represents AB and blue line represents CD .

The lines are perpendicular.