Plot the point on the polar coordinate system.
$(-2,\frac{2\pi}{3})$

• A.
• B.
• C.
• D.

Answer: (D)

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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).
5. 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, \(\frac{2\pi}{3}\)).