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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 point is (-2, \(\frac{2\pi}{3}\)). The negative radius means we will plot the point 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 counterclockwise from the positive x-axis.
Since the radius is negative, move 2 units in the opposite direction of \(\frac{2\pi}{3}\), which is equivalent to moving 2 units in the direction of \(\frac{5\pi}{3}\) (or 300 degrees).
Plot the point 2 units away from the origin in the direction of \(\frac{5\pi}{3}\). This is the correct location for the point (-2, \(\frac{2\pi}{3}\)).