Chapter 13.5, Problem 4ST1

a.

To determine

To find: the distance between the two points

Answer to Problem 4ST1

The distance between the two points is $\sqrt{29}$

Explanation of Solution

Given information: The points are $\left(-3,2\right)\&\left(-5,7\right)$

Calculation:

The distance between two points

  $\begin{array}{l}\overline{AB}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{AB}=\sqrt{{\left(-5-\left(-3\right)\right)}^2+{\left(7-2\right)}^2}\\ \overline{AB}=\sqrt{4+25}=\sqrt{29}\\ \overline{AB}=\sqrt{29}\end{array}$

b.

To determine

To find: the midpoint of the segment

Answer to Problem 4ST1

The midpoint of the segment is $\left(-4,4.5\right)$

Explanation of Solution

Given information: The points are $\left(-3,2\right)\&\left(-5,7\right)$

Calculation:

The midpoint of the segment

  $\begin{array}{l}M=\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2}\right)\\ M=\left(\frac{-3-5}{2},\frac{2+7}{2}\right)\\ M=\left(\frac{-8}{2},\frac{9}{2}\right)\\ M=\left(-4,4.5\right)\end{array}$