# How do you find the distance between (2/3,4) and (5/3,7)?

Feb 27, 2017

The distance, d, between two points, $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ is:

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

#### Explanation:

Using the distance formula with the given points, $\left(\frac{2}{3} , 4\right) \mathmr{and} \left(\frac{5}{3} , 7\right)$:

$d = \sqrt{{\left(\frac{5}{3} - \frac{2}{3}\right)}^{2} + {\left(7 - 4\right)}^{2}}$

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

$d = \sqrt{{\left(1\right)}^{2} + {\left(3\right)}^{2}}$

$d = \sqrt{1 + 9}$

$d = \sqrt{10}$