Chapter 9, Problem 1E

To determine

To find: The midpoint of the line segment given with end points $C=\left(5,-12\right)$ and $D=\left(-9,4\right)$ .

Answer to Problem 1E

The midpoint of the line segment given with end points $C=\left(5,-12\right)$ and $D=\left(-9,4\right)$ is $\left(-2,-4\right)$ .

Explanation of Solution

Given information:

The givenend points of the line segment are $C=\left(5,-12\right)$ and $D=\left(-9,4\right)$ .

Calculation:

Using the formula to calculate midpoint of the line segment with end points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is as.

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

Substitute the value in above equation.

  $\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{5+\left(-9\right)}{2},\frac{\left(-12\right)+4}{2}\right)\\ =\left(\frac{-4}{2},\frac{-8}{2}\right)\\ =\left(-2,-4\right)\end{array}$

Therefore, the midpoint of the line segment given with end points $C=\left(5,-12\right)$ and $D=\left(-9,4\right)$ is $\left(-2,-4\right)$ .