# Question #23ae3

Nov 6, 2017

#### Explanation:

$A = \left(- 9 , - 6\right)$
$B = \left(- 5 , 0\right)$
$C = \left(10 , - 7\right)$

Find the length of line segments $\overline{A B}$, $\overline{B C}$, and $\overline{A C}$

${d}_{A B}$
$= \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
$= \sqrt{{\left(\left(- 5\right) - \left(- 9\right)\right)}^{2} + {\left(\left(0\right) - \left(- 6\right)\right)}^{2}}$
$= \sqrt{{\left(4\right)}^{2} + {\left(6\right)}^{2}}$
$= \sqrt{16 + 36}$
$= \sqrt{52}$
etc.

${d}_{A B} = \sqrt{52}$
${d}_{B C} = \sqrt{274}$
${d}_{A C} = \sqrt{362}$
Total $= \sqrt{52} + \sqrt{274} + \sqrt{362} \approx 42.7903455$