Chapter 13.5, Problem 9PSB

(a)

To determine

To find:The midpoint.

Answer to Problem 9PSB

The midpoint of AB is $\left(5,6,-2\right)$

Explanation of Solution

Given:

The point is given as,

  $\begin{array}{l}A=\left[2,3,-5\right]\\ B=\left[8,9,1\right]\\ C=\left[3,17,1\right]\end{array}$

Calculation:

Calculate the midpoint of AB.

  $\begin{array}{c}{\text{Mid}}_{\text{AB}}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)\\ =\left(\frac{10}{2},\frac{12}{2},-\frac{4}{2}\right)\\ =\left(5,6,-2\right)\end{array}$

Thus, the midpoint of AB is $\left(5,6,-2\right)$

(b)

To determine

To find:The length of the medium from C

Answer to Problem 9PSB

The length of the medium from C is 11.6

Explanation of Solution

Given:

The point is given as,

  $\begin{array}{l}A=\left[2,3,-5\right]\\ B=\left[8,9,1\right]\\ C=\left[3,17,1\right]\end{array}$

Calculation:

Calculate the midpoint of AB.

  $\begin{array}{c}\text{CD}=\sqrt{{\left(5-3\right)}^2+{\left(6-17\right)}^2+{\left(-2-1\right)}^2}\\ =\sqrt{{\left(2\right)}^2+{\left(-11\right)}^2+{\left(-3\right)}^2}\\ =\sqrt{134}\\ =11.6\end{array}$

Thus, the length of the medium from C is 11.6