# What is the distance between (1,-4) and (7,5)?

May 31, 2017

10.82

#### Explanation:

The distance formula:

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

First arrange the coordinates as ${x}_{1}$, ${y}_{1}$ etc..

${x}_{1} = 1$
${y}_{1} = - 4$
${x}_{2} = 7$
${y}_{2} = 5$

Now substitute the values into the equation:

$\sqrt{{\left(7 - 1\right)}^{2} + {\left(5 - \left(- 4\right)\right)}^{2}}$

= $\sqrt{36 + 81}$

= $\sqrt{117}$

= 10.82