Chapter 8.4, Problem 42E

To determine

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

Answer to Problem 42E

  $\begin{array}{c}\text{Ordered pair}=\langle -8,-5\rangle \\ \text{Magnitude}=\sqrt{89}\end{array}$

Explanation of Solution

Given information:

The graph shown below represents the point of location of $D$ and $E$ .

The points given in the graph are $D\left(8,3\right)$ and $E\left(0,-2\right)$ .

Calculation:

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

  $\begin{array}{c}\overrightarrow{DE}=\langle x_2-x_1,y_2-y_1\rangle \\ =\langle 0-8,-2-3\rangle \left[\text{Put ordered pairs of }D\text{ and }E\right]\\ =\langle -8,-5\rangle \end{array}$

Thus the ordered pair is $\langle -8,-5\rangle$ .

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

  $\begin{array}{c}\left|\overrightarrow{DE}\right|=\sqrt{{\left({\overrightarrow{DE}}_x\right)}^2+{\left({\overrightarrow{DE}}_y\right)}^2}\\ =\sqrt{{\left(-8\right)}^2+{\left(-5\right)}^2}\left[\text{Put the ordered pairs of }\overrightarrow{DE}\right]\\ =\sqrt{64+25}\\ =\sqrt{89}\end{array}$

Thus the magnitude is $\sqrt{89}$ .