College Algebra, Chapter 2, 2.1, Section 2.1, Problem 30

(a) Plot the points $(-1,6),(-1,-3)$ 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{(0)^2 + (-9)^2}\\
\\
d &= \sqrt{(-9)^2}\\
\\
d &= 9 \text{ units}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } x &= \frac{-1+(-1)}{2} = -1\\
\\
y &= \frac{6-3}{2} = \frac{3}{2}
\end{aligned}
\end{equation}
$

Thus, the midpoint is $\left( -1,\frac{3}{2} \right)$