# What is the distance between (–2, 3) and (–2, –7)?

May 16, 2016

distance$= 10$

#### Explanation:

Start by labelling each coordinate.

$\left({x}_{1} , {y}_{1}\right) = \left(\textcolor{red}{- 2} , \textcolor{b l u e}{3}\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{- 2} , \textcolor{p u r p \le}{- 7}\right)$

Using the distance formula,

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

substitute the variables into the formula to find the distance between the two coordinates.

Thus,

$d = \sqrt{{\left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{- 2} - \left(\textcolor{red}{- 2}\right)\right)}^{2} + {\left(\textcolor{p u r p \le}{- 7} - \textcolor{b l u e}{3}\right)}^{2}}$

$d = \sqrt{{\left(- 2 + 2\right)}^{2} + {\left(- 10\right)}^{2}}$

$d = \sqrt{0 + 100}$

$d = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{10} \textcolor{w h i t e}{\frac{a}{a}} |}}}$