College Algebra, Chapter 2, 2.1, Section 2.1, Problem 22

Below is the graph of two points (a) Find the distance between them. (b) Find the midpoint of the segment that joins them.



a.) The points are $(2,2)$ and $(-2,1)$. By using distance formula.

$
\begin{equation}
\begin{aligned}
d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\
\\
d &= \sqrt{(-2,-2)^2 + (1-2)^2}\\
\\
d &= \sqrt{(-4)^2 + (-1)^2}\\
\\
d &= \sqrt{16+1}\\
\\
d &= \sqrt{17} \text{ units}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{b.) } x &= \frac{2-2}{2} = 0\\
\\
y &= \frac{2+1}{2} = \frac{3}{2}
\end{aligned}
\end{equation}
$

Thus, the midpoint is $\left( 0, \frac{3}{2} \right)$