Chapter 12, Problem 16CLT

To determine

Find the midpoint of the line segment joining.

Answer to Problem 16CLT

The coordinates are $\boxed{-1,2,\frac{1}{2}}$

Explanation of Solution

Given information:

Find the midpoint of the line segment joining $\left(3,4,-1\right)$ and $\left(-5,0,2\right)$ .

Calculation:

Consider the given points,

  $\left(3,4,-1\right)$

  $\left(-5,0,2\right)$

To find the coordinates of the midpoint of line joining use the standard formula,

The midpoint of line joining of two given points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ is

  $\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}$

Now substitute the coordinate’s value in formula.

  $\begin{array}{l}\frac{3-5}{2},\frac{4+0}{2},\frac{-1+2}{2}\\ =\frac{-2}{2},\frac{4}{2},\frac{1}{2}\\ =-1,2,\frac{1}{2}\end{array}$

Hence the midpoint of line joining is $\boxed{-1,2,\frac{1}{2}}$