# What is the distance between (15,24) and (42,4)?

Nov 23, 2015

The distance between $\left(15 , 24\right)$ and $\left(42 , 4\right)$ is approximately $33.6$ units.

#### Explanation:

The formula for the distance between $2$ points is:

$d = \sqrt{\left({\left({x}_{\text{2"-x_"1")^2+(y_"2"-y_"1}}\right)}^{2}\right)}$

${1}^{s t}$ point: $\left({x}_{\text{1",y_"1}}\right)$ = $\left(15 , 24\right)$
${2}^{n d}$ point: $\left({x}_{\text{2",y_"2}}\right)$ = $\left(42 , 4\right)$

Substitute the points into the distance formula:

$d = \sqrt{\left({\left({x}_{\text{2"-x_"1")^2+(y_"2"-y_"1}}\right)}^{2}\right)}$
$d = \sqrt{{\left(\left(42\right) - \left(15\right)\right)}^{2} + {\left(\left(4\right) - \left(24\right)\right)}^{2}}$
$d = \sqrt{{\left(27\right)}^{2} + {\left(- 20\right)}^{2}}$
d=sqrt((729)+(400)
$d = \sqrt{1129}$
$d \approx 33.6$