Chapter 11.4, Problem 74E

To determine

To find whether AB and CD are parallel or opposite or neither of these.

Answer to Problem 74E

Parallel.

Explanation of Solution

Given:

The given points are $A(-2,5),B(3,-1),C(2,6)$ and $D(7,0)$

Calculation:

The magnitude of line AB is

  $\begin{array}{l}AB=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}\\ AB=\sqrt{{(-2-3)}^2+{(5+1)}^2}\\ AB=\sqrt{25+36}\\ AB=\sqrt{61}\end{array}$

The magnitude of line BC is

  $\begin{array}{l}CD=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}\\ CD=\sqrt{{(2-7)}^2+{(6-0)}^2}\\ CD=\sqrt{25+36}\\ CD=\sqrt{61}\end{array}$

The angle between the lines is −

  $\begin{array}{l}\cos \theta =\frac{\left|AB\right|}{\left|CD\right|}\\ \cos \theta =1\\ \Rightarrow \theta =0\end{array}$

Therefore the given lines are parallel.