Chapter 8.2, Problem 21E

To determine

To find: the ordered pair and magnitude of $\overrightarrow{YZ}$ .

Answer to Problem 21E

  $\begin{array}{c}\text{Ordered pair}=\langle 9,9\rangle \\ \text{Magnitude}=9\sqrt{2}\end{array}$

Explanation of Solution

Given information:

  $Y\left(14,-23\right),Z\left(23,-14\right)$

Calculation:

The ordered pair of $\overrightarrow{YZ}$ is evaluated as follows:

  $\begin{array}{c}\overrightarrow{YZ}=\langle x_2-x_1,y_2-y_1\rangle \\ =\langle 23-14,-14-\left(-23\right)\rangle \left[\text{Put ordered pairs of }Z\text{ and }Y\right]\\ =\langle 9,9\rangle \end{array}$

Thus the ordered pair is $\langle 9,9\rangle$ .

The magnitude of $\overrightarrow{YZ}$ is evaluated as follows:

  $\begin{array}{c}\left|\overrightarrow{YZ}\right|=\sqrt{{\left({\overrightarrow{YZ}}_x\right)}^2+{\left({\overrightarrow{YZ}}_y\right)}^2}\\ =\sqrt{{\left(9\right)}^2+{\left(9\right)}^2}\left[\text{Put the ordered pairs of }\overrightarrow{YZ}\right]\\ =\sqrt{162}\\ =9\sqrt{2}\end{array}$

Thus the magnitude is $9\sqrt{2}$ .