# What is the distance between the following polar coordinates?:  (1,pi/2), (-1,pi/2)

There must a mistake, polar coordinates of a point are given in the form $\left(\rho , \theta\right)$, where $\rho$ is the distance from the origin, and $\theta$ is the angle formed with the $x$-axis. So, $\rho$ can't be negative.
$\left(1 , \setminus \frac{\pi}{2}\right)$ and $\left(1 , - \setminus \frac{\pi}{2}\right)$,
then you can work like this: since $\rho = 1$, both points are in the unit circle. And in particular, they are opposite points, since ${90}^{\circ}$ and $- {90}^{\circ}$ determine the "north pole" and "south pole" of the circle. So, the distance between them is two times the radius, which is $2$.