Chapter 13.5, Problem 3ST1

a.

To determine

To find: the distance between the two points

Answer to Problem 3ST1

The distance between the two points is $10\sqrt{2}$

Explanation of Solution

Given information: The points are $\left(-2,7\right)\&\left(8,-3\right)$

Calculation:

The distance between two points

  $\begin{array}{l}\overline{AB}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{AB}=\sqrt{{\left(8-\left(-2\right)\right)}^2+{\left(7-\left(-3\right)\right)}^2}\\ \overline{AB}=\sqrt{100+100}=\sqrt{200}\\ \overline{AB}=10\sqrt{2}\end{array}$

b.

To determine

To find: the midpoint of the segment

Answer to Problem 3ST1

The midpoint of the segment is $\left(3,2\right)$

Explanation of Solution

Given information: The points are $\left(-2,7\right)\&\left(8,-3\right)$

Calculation:

The midpoint of the segment

  $\begin{array}{l}M=\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2}\right)\\ M=\left(\frac{-2+8}{2},\frac{7-3}{2}\right)\\ M=\left(\frac{6}{2},\frac{4}{2}\right)\\ M=\left(3,2\right)\end{array}$