Chapter 11, Problem 5CLT

To determine

To calculate:

The midpoint of the line segment for the following points

  $\begin{array}{l}\left(3,4,-1\right)\\ \left(-5,0,2\right)\end{array}$

Answer to Problem 5CLT

The midpoint of the line segment $\left(3,4,-1\right)$ and $\left(-5,0,2\right)$ is $\left(-1,2,\frac{1}{2}\right)$ .

Explanation of Solution

Given information:

  $\begin{array}{l}A=\left(3,4,-1\right)\\ B=\left(-5,0,2\right)\end{array}$

Formula Used:

By using the formula:

  $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$

Calculation:

The midpoint of the line segments the points:

  $\begin{array}{l}A=\left(x_1,y_1,z_1\right)\\ B=\left(x_2,y_2,z_2\right)\end{array}$

By using the formula:

  $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$

Put the value in formula:

  $\begin{array}{l}M=\left(\frac{3+\left(-5\right)}{2},\frac{4+0}{2},\frac{-1+2}{2}\right)\\ M=\left(\frac{-2}{2},\frac{4}{2},\frac{1}{2}\right)\\ M=\left(-1,2,\frac{1}{2}\right)\end{array}$

Therefore, the midpoint of the line segment $\left(3,4,-1\right)$ and $\left(-5,0,2\right)$ is $\left(-1,2,\frac{1}{2}\right)$ .