Chapter 3.3, Problem 31PPS

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 31PPS

The lines are perpendicular.

Explanation of Solution

Given information:

  $A(8,-2),B(4,-1),C(3,11),D(-2,-9)$

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 ,

  $x_1^{}=8,y_1^{}=-2$

  $x_2^{}=4,y_2^{}=-1$

Substituting value,

Slope of line is, $m=\frac{-1-(-2)}{4-8}$

Solving,

$m=\frac{-1+2}{-4}$

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

For CD ,

  $x_1^{}=3,y_1^{}=11$

  $x_2^{}=-2,y_2^{}=-9$

Substituting value,

Slope of line is, $m=\frac{-9-11}{-2-3}$

Solving,

$m=\frac{-20}{-5}$

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.