Chapter 8.3, Problem 41E

To determine

The midpoint and distance between the two points.

Answer to Problem 41E

  $\left(\frac{a+c}{2},c\right)$

  $\left|b-a\right|$

Explanation of Solution

Given:

The given points are:

  $\left(a,c\right)\text{and}\left(b,c\right)$

Calculation:

The midpoint is given by:

  $\begin{array}{l}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{a+c}{2},\frac{c+c}{2}\right)\\ =\left(\frac{a+c}{2},c\right)\end{array}$

The distance between the points will be:

  $\begin{array}{l}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(b-a\right)}^2+{\left(c-c\right)}^2}\\ =\sqrt{{\left(b-a\right)}^2+{\left(0\right)}^2}\\ =\left|b-a\right|\end{array}$