Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 4

a. Find the distance between the points $(-2,2)$ and $(1,4)$.

Using the Distance Formula,


$\begin{equation} \begin{aligned} d =& \sqrt{(-2-1)^2 + (2-4)^2} \\ d =& \sqrt{9+4} \\ d =& \sqrt{13} \end{aligned} \end{equation}$


b. Find the midpoint of the given points.

Using the Midpoint Formula,


$\begin{equation} \begin{aligned} M = (x,y) =& \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \\ \\ =& \left( \frac{-2+1}{2}, \frac{2+4}{2} \right) \\ \\ =& \left( \frac{-1}{2}, 3 \right) \end{aligned} \end{equation}$


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

Using the Formula for Slope,


$\begin{equation} \begin{aligned} m =& \frac{y_2- y_1}{x_2 - x_1} \\ \\ =& \frac{4-2}{1-(-2)} \\ \\ =& \frac{6}{3} \\ \\ =& 2 \end{aligned} \end{equation}$


d. Interpret the slope in part (c).

For every increment of $x$ by 1 unit, $y$ will increase by 2 units.