# What is the distance between (4, 2)  and  (-5, -2) ?

May 26, 2016

The distance is approximately 9.84.

#### Explanation:

If you have two points with coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the distance is given by the Pitagora's theorem as:

$d = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$.
For you this mean
$d = \sqrt{{\left(4 + 5\right)}^{2} + {\left(2 + 2\right)}^{2}} = \sqrt{{9}^{2} + {4}^{2}} = \sqrt{81 + 16} = \sqrt{97} \setminus \approx 9.84$.

Be careful when you apply this formula that you have to use the correct signs. For example I have that the $x$ coordinate of the second point is ${x}_{2} = - 5$. In the formula I have ${x}_{1} - {x}_{2}$ that is ${x}_{1} - \left(- 5\right)$ and the double minus results in a +. This is why you see it with a plus sign.