Chapter 8, Problem 22SGA

To determine

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

Answer to Problem 22SGA

  $\begin{array}{c}\text{Ordered pair}=\langle 1,-8\rangle \\ \text{Magnitude}=\sqrt{67}\end{array}$

Explanation of Solution

Given information:

  $C\left(-6,4\right),D\left(-5,-4\right)$

Calculation:

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

  $\begin{array}{c}\overrightarrow{CD}=\langle x_2-x_1,y_2-y_1\rangle \\ =\langle -5-\left(-6\right),-4-4\rangle \left[\text{Put ordered pairs of }C\text{ and }D\right]\\ =\langle 1,-8\rangle \end{array}$

Thus the ordered pair is $\langle 1,-8\rangle$ .

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

  $\begin{array}{c}\left|\overrightarrow{CD}\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(1\right)}^2+{\left(-8\right)}^2}\left[\text{Put the ordered pairs of }\overrightarrow{CD}\right]\\ =\sqrt{1+64}\\ =\sqrt{67}\end{array}$

Thus the magnitude is $\sqrt{67}$ .