What is the distance between (–2, 2, 6)  and (–5, –1, 1) ?

Mar 7, 2018

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 5} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{- 1} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{1} - \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 5} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{- 1} - \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{1} - \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{\left(- 3\right)}^{2} + {\left(- 3\right)}^{2} + {\left(- 5\right)}^{2}}$

$d = \sqrt{9 + 9 + 25}$

$d = \sqrt{43}$