# How do you find the distance between (4/5, -1), (2,-1/2)?

Feb 1, 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 and calculating gives:

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{\frac{4}{5}}\right)}^{2} + {\left(\textcolor{red}{- \frac{1}{2}} - \textcolor{b l u e}{- 1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{\frac{4}{5}}\right)}^{2} + {\left(\textcolor{red}{- \frac{1}{2}} + \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{2} - \textcolor{b l u e}{0.8}\right)}^{2} + {\left(\textcolor{red}{- 0.5} + \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(1.2\right)}^{2} + {\left(0.5\right)}^{2}}$

$d = \sqrt{1.44 + 0.25}$

$d = \sqrt{1.69} = 1.3$

$d = 1 + \frac{3}{10}$

$d = \frac{10}{10} + \frac{3}{10}$

$d = \frac{13}{10}$

The distance between the points is $1.3$ or $\frac{13}{10}$