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.