Chapter 9.1, Problem 46HP

To determine

To find: The reason for the midpoint formula is used to approximate the halfway points.

Answer to Problem 46HP

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

Explanation of Solution

Calculation:

The midpoint formula is given as,

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

Take two points,

  $\begin{array}{l}\left(x_1,y_1\right)=\left(2,4\right)\\ \left(x_2,y_2\right)=\left(78,46\right)\end{array}$

Substitute the values.

  $\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{2+78}{2},\frac{4+46}{2}\right)\\ =\left(\frac{80}{2},\frac{50}{2}\right)\\ =\left(40,25\right)\end{array}$

Thus, the midpoint is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ .