Chapter 8.3, Problem 15Q

To determine

The coordinates of the midpoint.

The distance between two points.

Answer to Problem 15Q

  $\left(3,0\right)$

  $\sqrt{40}$

Explanation of Solution

Given:

The given points are:

  $\begin{array}{l}J\left(4,3\right)\\ K\left(2,-3\right)\end{array}$

Calculation:

The coordinates of midpoint will be:

  $\begin{array}{l}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{4+2}{2},\frac{3+\left(-3\right)}{2}\right)\\ =\left(3,0\right)\end{array}$

The distance between the points is:

  $\begin{array}{l}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(2-4\right)}^2+{\left(-3-3\right)}^2}\\ =\sqrt{{\left(-2\right)}^2+{\left(-6\right)}^2}\\ =\sqrt{4+36}\\ =\sqrt{40}\end{array}$