Chapter 11.1, Problem 45E

To determine

Tofind:Themidpoint of the line segment joining the points $\left(-5,-2,5\right)$ and $\left(6,3,-7\right)$ .

Answer to Problem 45E

Themidpoint of the line segment joining the points $\left(-5,-2,5\right)$ and $\left(6,3,-7\right)$ is $\left(\frac{1}{2},\frac{1}{2},-1\right)$ .

Explanation of Solution

Given information:

The given points are $\left(-5,-2,5\right)$ and $\left(6,3,-7\right)$ .

Calculation:

The midpointof the line segment joining the two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ can be calculated by the midpoint formula in space.

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

Let $\left(x_1,y_1,z_1\right)=\left(-5,-2,5\right)$ and $\left(x_2,y_2,z_2\right)=\left(6,3,-7\right)$ are the two points.

Substitute the values in the above formula to calculate the midpoint.

  $\begin{array}{c}\text{Midpoint}=\left(\frac{-5+6}{2},\frac{-2+3}{2},\frac{5+\left(-7\right)}{2}\right)\\ =\left(\frac{1}{2},\frac{1}{2},-\frac{2}{2}\right)\\ =\left(\frac{1}{2},\frac{1}{2},-1\right)\end{array}$

Therefore, themidpoint of the line segment joining the points $\left(-5,-2,5\right)$ and $\left(6,3,-7\right)$ is $\left(\frac{1}{2},\frac{1}{2},-1\right)$ .