# How do you use the distance formula find the distance, to the nearest tenth from J (4,-2) and U (-2,3)?

Jun 12, 2017

See a solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 2} - \textcolor{b l u e}{4}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{- 2}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 2} - \textcolor{b l u e}{4}\right)}^{2} + {\left(\textcolor{red}{3} + \textcolor{b l u e}{2}\right)}^{2}}$

Next, perform the addition and subtraction of the terms within the parenthesis:

$d = \sqrt{{\left(- 6\right)}^{2} + {5}^{2}}$

Then square each term within the radical:

$d = \sqrt{36 + 25}$

$d = \sqrt{61}$
$d = 7.8$