Chapter 13.5, Problem 1ST1

a.

To determine

To find: the distance between the two points

Answer to Problem 1ST1

The distance between the two points is $2$

Explanation of Solution

Given information: The points are $\left(5,1\right)\&\left(3,1\right)$

Calculation:

The distance between two points

  $\begin{array}{l}\overline{AB}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{AB}=\sqrt{{\left(5-3\right)}^2+{\left(1-1\right)}^2}\\ \overline{AB}=\sqrt{{\left(2\right)}^2}=\sqrt{4}\\ \overline{AB}=2\end{array}$

b.

To determine

To find: the midpoint of the segment

Answer to Problem 1ST1

The midpoint of the segment is $\left(4,1\right)$

Explanation of Solution

Given information: The points are $\left(5,1\right)\&\left(3,1\right)$

Calculation:

The midpoint of the segment

  $\begin{array}{l}M=\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2}\right)\\ M=\left(\frac{5+3}{2},\frac{1+1}{2}\right)\\ M=\left(\frac{8}{2},\frac{2}{2}\right)\\ M=\left(4,1\right)\end{array}$