# How do you find the distance between (-2,-3) and (-2,4)?

Feb 5, 2017

See the entire 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 problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 2} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{- 3}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 2} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{4} + \textcolor{b l u e}{3}\right)}^{2}}$

$d = \sqrt{{0}^{2} + {7}^{2}}$

$d = \sqrt{0 + 49}$

$d = \sqrt{49} = 7$