Determine if the given polar coordinates represent the same point.
-(r, $\theta$), (-r, $\theta$ + $\pi$)

Question

Quizplus · Accepted Answer

In polar coordinates, a point defined by $(r, \theta)$ can also be represented as $(-r, \theta + \pi)$ because adding $\pi$ to the angle $\theta$ effectively rotates the point 180 degrees around the origin, which is the same as changing the direction of the radius $r$ to its opposite, hence pointing to the same location in the plane.

Determine If the Given Polar Coordinates Represent the Same Point θ\thetaθ

Determine If the Given Polar Coordinates Represent the Same Point $\theta$