Chapter 9.1, Problem 13OE

To determine

To calculate: The midpoint of the line segment.

Answer to Problem 13OE

The coordinates of the midpoint are $\left(-0.5,-1.5\right)$ .

Explanation of Solution

Given information: The coordinates of two points are $\left(5,-1\right)$ and $\left(-6,-2\right)$ .

Formula used: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation: Let the line segment joining the point $P\left(5,-1\right),Q\left(-6,-2\right)$ and its midpoint be M.

So,

  $\begin{array}{cc}P& Q\\ x_1=5& x_2=-6\\ y_1=-1& y_2=-2\end{array}$

Put the value of x and y coordinates into the formula $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ .

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{5-6}{2},\frac{-1-2}{2}\right).\\ M=\left(\frac{-1}{2},\frac{-3}{2}\right)\\ M=\left(-0.5,-1.5\right)\end{array}$

Thus, the coordinates of the midpoint of the line segment are $\left(-0.5,-1.5\right)$ .