Chapter 3.3, Problem 3BCYP

To determine

To tell whether lines are perpendicular, parallel or neither.

Answer to Problem 3BCYP

The lines are parallel.

Explanation of Solution

Given information:

  $A(3,6),B(-9,2),C(5,4),D(2,3)$

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 AB,

  $x_1^{}=3,y_1^{}=6$

  $x_2^{}=-9,y_2^{}=2$

Substituting value,

Slope of line is, $m=\frac{-9-3}{2-6}$

Solving,

$m=\frac{-12}{-4}$

Slope for AB is 3.

For CD,

  $x_1^{}=5,y_1^{}=4$

  $x_2^{}=2,y_2^{}=3$

Substituting value,

Slope of line is, $m=\frac{2-5}{3-4}$

Solving,

$m=\frac{-3}{-1}$

Slope is3.

Now, line is parallel as slope is equal.