# What is the distance between the following polar coordinates?:  (2,(3pi)/2), (-2,pi/2)

Apr 14, 2017

distance $= 0$

#### Explanation:

$\left(2 , \frac{3 \pi}{2}\right)$ is located at a distance of $2$ from $\left(0 , 0\right)$ at the angle $\frac{3 \pi}{2} = {270}^{\circ}$ counter-clockwise from the $x$-axis.

$\left(2 , \frac{\pi}{2}\right)$ is located at a distance of $2$ from $\left(0 , 0\right)$ at an angle of $\frac{\pi}{2} = {90}^{\circ}$. The $- 2$ means ${180}^{\circ}$ from the location $\left(2 , \frac{\pi}{2}\right)$.
${180}^{\circ}$ from ${90}^{\circ} = {270}^{\circ} = \frac{3 \pi}{2}$

This means $\left(- 2 , \frac{\pi}{2}\right) = \left(2 , \frac{3 \pi}{2}\right)$

The distance would $= 0$ because they are the same point.