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

1 Answer
Dec 14, 2015

There must a mistake, polar coordinates of a point are given in the form #(rho, theta)#, where #rho# is the distance from the origin, and #theta# is the angle formed with the #x#-axis. So, #rho# can't be negative.

If you wanted to know the distance between

#(1,\pi/2)# and #(1,-\pi/2)#,

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^@# and #-90^@# determine the "north pole" and "south pole" of the circle. So, the distance between them is two times the radius, which is #2#.