Chapter 11.1, Problem 43E

To determine

Tofind:Themidpoint of the line segment joining the points $\left(3,-6,10\right)$ and $\left(-3,4,4\right)$ .

Answer to Problem 43E

Themidpoint of the line segment joining the points $\left(3,-6,10\right)$ and $\left(-3,4,4\right)$ is $\left(0,-1,7\right)$ .

Explanation of Solution

Given information:

The given points are $\left(3,-6,10\right)$ and $\left(-3,4,4\right)$ .

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 $\left(x_1,y_1,z_1\right)=\left(3,-6,10\right)$ and $\left(x_2,y_2,z_2\right)=\left(-3,4,4\right)$ are the two points.

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

  $\begin{array}{c}\text{Midpoint}=\left(\frac{3+\left(-3\right)}{2},\frac{-6+4}{2},\frac{10+4}{2}\right)\\ =\left(\frac{0}{2},-\frac{2}{2},\frac{14}{2}\right)\\ =\left(0,-1,7\right)\end{array}$

Therefore, themidpoint of the line segment joining the points $\left(3,-6,10\right)$ and $\left(-3,4,4\right)$ is $\left(0,-1,7\right)$ .