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Multiple Choice
Plot the point on the polar coordinate system. (−2,32π)
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Verified step by step guidance
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Understand that polar coordinates are given in the form (r, θ), where r is the radius (distance from the origin) and θ is the angle from the positive x-axis.
The given polar coordinate is (-2, \frac{2\pi}{3}). The negative radius indicates that the point is in the opposite direction of the angle.
First, locate the angle \frac{2\pi}{3} on the polar coordinate system. This angle is in the second quadrant, 120 degrees from the positive x-axis.
Since the radius is negative, move 2 units in the opposite direction of the angle \frac{2\pi}{3}. This means you will move 2 units in the direction of the angle \frac{5\pi}{3} (or 300 degrees), which is directly opposite to \frac{2\pi}{3}.
Plot the point at this location, which should be in the fourth quadrant, 2 units from the origin along the line of \frac{5\pi}{3}.