Chapter 9.1, Problem 14OE

To determine

To calculate: The midpoint of the line segment.

Answer to Problem 14OE

The coordinates of the midpoint are $\left(4.5,1.75\right)$ .

Explanation of Solution

Given information: The coordinates of two points are $\left(2.5,0.5\right)$ and $\left(6.5,3\right)$ .

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 $P\left(2.5,0.5\right),Q\left(6.5,3\right)$ and its midpoint be M.

So,

  $\begin{array}{cc}P& Q\\ x_1=2.5& x_2=6.5\\ y_1=0.5& y_2=3\end{array}$

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

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{2.5+6.5}{2},\frac{0.5+3}{2}\right).\\ M=\left(\frac{9}{2},\frac{3.5}{2}\right)\\ M=\left(4.5,1.75\right)\end{array}$

Thus, the coordinates of the midpoint of the line segment are $\left(4.5,1.75\right)$ .