Chapter 11.2, Problem 4E

To determine

To Find:The vector $\overrightarrow{OP}$ where $P$ is the midpoint of $RS$ .

Answer to Problem 4E

The required vector is $\langle -1,1\rangle$ .

Explanation of Solution

Given Information:

  $\begin{array}{l}R=\left(2,-1\right)\\ S=(-4,3)\end{array}$

  $P$ is the midpoint of $RS$

Formula Used:

Midpoint of a line is

  $M=\left(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}\right)$

Here, $M$ is the slope and $x_1,x_2,y_1,y_2$ points.

Calculation:

Substitute $2,-4$ for $x_1,x_2$ and $-1,3$ for $y_1,y_2$ in the midpoint equation.

  $\begin{array}{c}M=\left(\frac{-4+2}{2},\frac{3-1}{2}\right)\\ =\left(-1,1\right)\end{array}$

Subtract origin from the midpoint

  $\begin{array}{l}\langle -1-0,1-0\rangle \\ \langle -1,1\rangle \end{array}$

Conclusion:

Hence, the required vector is $\langle -1,1\rangle$ .