Chapter 8.2, Problem 4CFU

To determine

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

Answer to Problem 4CFU

  $\begin{array}{c}\text{Ordered pair}=\langle -5,5\rangle \\ \text{Magnitude}=5\sqrt{2}\end{array}$

Explanation of Solution

Given information:

  $M\left(2,-1\right),P\left(-3,4\right)$

Calculation:

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

  $\begin{array}{c}\overrightarrow{MP}=\langle x_2-x_1,y_2-y_1\rangle \\ =\langle -3-2,4-\left(-1\right)\rangle \left[\text{Put ordered pairs of }P\text{ and }M\right]\\ =\langle -5,4+1\rangle \\ =\langle -5,5\rangle \end{array}$

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

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

  $\begin{array}{c}\left|\overrightarrow{MP}\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-5\right)}^2+{\left(5\right)}^2}\left[\text{Put the ordered pairs of }MP\right]\\ =\sqrt{50}\\ =5\sqrt{2}\end{array}$

Thus the magnitude is

  $5\sqrt{2}$ .