Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 2

a. Find the distance between the points $(0,0)$ and $(-4,6)$.

Using the Distance Formula,


$\begin{equation} \begin{aligned} d =& \sqrt{(-4-0)^2 + (6-0)^2} \\ d =& \sqrt{16 + 36} \\ d =& \sqrt{52} \\ d =& 2 \sqrt{13} \end{aligned} \end{equation}$


b. Find the midpoint of the given points.

Using the Midpoint Formula,


$\begin{equation} \begin{aligned} M = (x,y) =& \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \\ \\ =& \left( \frac{0+ (-4)}{2}, \frac{0+6}{2} \right) \\ \\ =& \left( \frac{-4}{2}, \frac{6}{2} \right) \\ \\ =& (-2,3) \end{aligned} \end{equation}$


c. Find the slope of the line containing the given points.

Using the Formula for Slope,


$\begin{equation} \begin{aligned} m =& \frac{y_2- y_1}{x_2 - x_1} \\ \\ =& \frac{6-0}{-4-0} \\ \\ =& \frac{6}{-4} \\ \\ =& \frac{3}{-2} \\ \\ =& - \frac{3}{2} \end{aligned} \end{equation}$


d. Interpret the slope in part (c).

For every decrements of $x$ by 2 units, $y$ will increase by 3 units.