# How do you find the distance between (5,-1/2) and (-3,5/2)?

Feb 17, 2017

See the entire 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:

$d = \sqrt{{\left(\textcolor{red}{- 3} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{\frac{5}{2}} - \textcolor{b l u e}{- \frac{1}{2}}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 3} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{\frac{5}{2}} + \textcolor{b l u e}{\frac{1}{2}}\right)}^{2}}$

$d = \sqrt{{\left(- 8\right)}^{2} + {\left(\frac{6}{2}\right)}^{2}}$

$d = \sqrt{{\left(- 8\right)}^{2} + {3}^{2}}$

$d = \sqrt{64 + 9}$

$d = \sqrt{73} = 8.544$ rounded to the nearest thousandth.

Feb 17, 2017

Using the Distance Formula,
$\text{the reqd. Distance=} \sqrt{{\left(5 - \left(- 3\right)\right)}^{2} + {\left(- \frac{1}{2} - \frac{5}{2}\right)}^{2}} = \sqrt{73}$
$\approx 8.544 \left(3 \mathrm{dp}\right) .$