# What is the distance between P(0, 0) and Q(5, 12)?

May 26, 2016

$13$

#### Explanation:

The distance between two points can be determined using the distance formula:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, to find the distance between the two given points, let:

• $\left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right) = \left(\textcolor{red}{0} , \textcolor{b l u e}{0}\right)$
• $\left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{{x}_{2}} , \textcolor{v i o \le t}{{y}_{2}}\right) = \left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{5} , \textcolor{v i o \le t}{12}\right)$

With these two points, substitute them into the distance formula.

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

$d = \sqrt{{\left(\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{5} - \textcolor{red}{0}\right)}^{2} + {\left(\textcolor{v i o \le t}{12} - \textcolor{b l u e}{0}\right)}^{2}}$

$d = \sqrt{{\left(5\right)}^{2} + {\left(12\right)}^{2}}$

$d = \sqrt{25 + 144}$

$d = \sqrt{169}$

$d = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{13} \textcolor{w h i t e}{\frac{a}{a}} |}}}$