Determine if the given polar coordinates represent the same point.
-$$( 2 , \pi / 4 ) , ( - 2 , - \pi / 4 )$$

Question

Quizplus · Accepted Answer

In polar coordinates, a negative radius flips the direction of the point across the origin. However, changing the angle by $\pi$ (or 180 degrees) is necessary to point in the exact opposite direction and thus represent the same point in Cartesian coordinates. Here, $-\pi/4$ is not sufficient to counteract the negative radius to point in the same direction as $\pi/4$, so they do not represent the same point.

Determine If the Given Polar Coordinates Represent the Same Point (2,π/4),(−2,−π/4)( 2 , \pi / 4 ) , ( - 2 , - \pi / 4 )(2,π/4),(−2,−π/4)

Determine If the Given Polar Coordinates Represent the Same Point $( 2 , \pi / 4 ) , ( - 2 , - \pi / 4 )$