College Algebra, Chapter 2, 2.1, Section 2.1, Problem 32

(a) Plot the points $(2,13),(7,1)$ in the coordinate plane. (b) Find the distance between them. c) Find the midpoint of the segment that joins them
a.)




b.) By using distance formula.

$
\begin{equation}
\begin{aligned}
d &= \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\
\\
d &= \sqrt{(7-2)^2 + (1-13)^2}\\
\\
d &= \sqrt{(5)^2 + (-12)^2}\\
\\
d &= \sqrt{25+144}\\
\\
d &= \sqrt{169}\\
\\
d &= 13 \text{ units}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } x &= \frac{2+7}{2} = \frac{9}{2}\\
\\
y &= \frac{13+1}{2} = \frac{14}{2} = 7
\end{aligned}
\end{equation}
$

Thus, the midpoint is $\left( \frac{9}{2},7 \right)$