# What is the distance between the following polar coordinates?:  (1,(pi)/8), (11,(5pi)/8)

Aug 5, 2016

Distance: color(green)(sqrt(122)

#### Explanation:

Note that these points (relative to the origin) are at right angles to each other (since $\frac{5 \pi}{8} - \frac{\pi}{8} = \frac{\pi}{2}$).

Therefore we are looking at a right triangle with arms of length $1$ and $11$
and a distance between them equal to the hypotenuse.

Using the Pythagorean Theorem, this distance is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{1}^{2} + {11}^{2}} = \sqrt{122}$