Here are the essential concepts you must grasp in order to answer the question correctly.
Polar Coordinates
Polar coordinates represent points in a plane using a distance from the origin and an angle from the positive x-axis. The format is (r, θ), where 'r' is the radial distance and 'θ' is the angle in radians. Understanding how to interpret these coordinates is essential for analyzing the given points.
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Intro to Polar Coordinates
Angle Representation
Angles in polar coordinates can be represented in multiple ways due to periodicity. For example, an angle θ and θ + 2πk (where k is any integer) represent the same direction. This concept is crucial for determining which representations of the given point maintain its location.
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Negative Radius in Polar Coordinates
In polar coordinates, a negative radius indicates a point that is in the opposite direction of the angle. For instance, (−r, θ) is equivalent to (r, θ + π). This understanding helps in identifying how the given points relate to each other and whether they represent the same location.
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Intro to Polar Coordinates