College Algebra, Exercise P, Exercise P.3, Section Exercise P.3, Problem 62

Determine the distance between



a.) $\displaystyle \frac{7}{5} \text{ and } -\frac{1}{21}$
Let $\displaystyle a = \frac{7}{5} \text{ and } b = -\frac{1}{21}$


$
\begin{equation}
\begin{aligned}
d (a, b) &= |b - a|\\
\\
&= \left| \frac{-1}{21}- \frac{7}{15} \right|\\
\\
&= \left| \frac{-1}{3 \cdot 7} - \frac{7}{3 \cdot 5} \right|\\
\\
&= \left| \frac{\frac{-5}{3}-\frac{49}{3}}{35}\right|\\
\\
&= \left| \frac{\frac{-5-49}{3}}{35} \right|\\
\\
&= \left| \frac{\frac{-54}{3}}{35} \right|\\
\\
&= \left| \frac{-18}{35} \right|\\
\\
&= \left( -\frac{18}{35} \right)\\
\\
&= \frac{18}{35}
\end{aligned}
\end{equation}
$

b.) $-38$ and $-57$
Let $a = -38 \text{ and } b = -57$

$
\begin{equation}
\begin{aligned}
d(a,b) &= |b-a|\\
\\
&= |-57 - (-38)|\\
\\
&= |-57 + 38|\\
\\
&= |-19|\\
\\
&= -(-19)\\
\\
&= 19
\end{aligned}
\end{equation}
$


c.) $-2.6$ and $-1.8$
Let $a = -2.6 \text{ and } b = -1.8$

$
\begin{equation}
\begin{aligned}
d(a,b) &= |b-a|\\
\\
&= |-1.8-(-2.6)|\\
\\
&= |-1.8 + 2.6|\\
\\
&= |0.8|\\
\\
&= 0.8
\end{aligned}
\end{equation}
$