Chapter 9.1, Problem 1AGP

To determine

To find: The coordinates of the midpoint of line segment $\overline{AB}$ .

Answer to Problem 1AGP

The midpoint is $\left(\frac{1}{2},10\right)$ .

Explanation of Solution

Given:

The given end points of line segment are:

  $\begin{array}{l}A\left(5,12\right)\\ B\left(-4,8\right)\end{array}$

The midpoint of line segment with end points is given as:

  $\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

The midpoint is calculated as:

  $\begin{array}{c}\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{5+\left(-4\right)}{2},\frac{12+8}{2}\right)\\ =\left(\frac{1}{2},10\right)\end{array}$

Therefore the midpoint is $\left(\frac{1}{2},10\right)$ .