# What is the distance between (2 , (3 pi)/4 ) and (-1 , pi )?

Jan 30, 2018

$\sqrt{5 + 2 \sqrt{2}}$

#### Explanation:

The polar point $\left(- 1 , \pi\right)$ is equivalent to the polar point $\left(1 , 0\right)$.

We can use the Law of Cosines to find the distance between the two points. Call the distance $c$, we have:

$c = \sqrt{{2}^{2} + {1}^{2} - 2 \left(2\right) \left(1\right) \cos \left(\frac{3 \pi}{4}\right)}$

$= \sqrt{4 + 1 - 4 \left(- \frac{\sqrt{2}}{2}\right)}$

$= \sqrt{5 + 2 \sqrt{2}}$