How do you find the distance between points (-7,8), (3,10)?

Aug 17, 2017

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{3} - \textcolor{b l u e}{- 7}\right)}^{2} + {\left(\textcolor{red}{10} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{3} + \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{10} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{10}^{2} + {2}^{2}}$

$d = \sqrt{100 + 4}$

$d = \sqrt{104}$

$d = \sqrt{4 \cdot 26}$

$d = \sqrt{4} \sqrt{26}$

$d = 2 \sqrt{26}$

Or

$d = 2 \cdot 5.099$

$d = 10.198$ rounded to the nearest thousandth.