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. Step 1: Understand the polar coordinate system. In polar coordinates, a point is represented as (r, θ), where 'r' is the radial distance from the origin and 'θ' is the angle measured counterclockwise from the positive x-axis.
2. Step 2: Analyze the given point (-2, 2π/3). The radial distance 'r' is negative, which means the point is located in the opposite direction of the angle θ. The angle θ = 2π/3 is measured counterclockwise from the positive x-axis.
3. Step 3: Locate the angle θ = 2π/3 on the polar coordinate system. This angle lies in the second quadrant, as it is between π/2 and π.
4. Step 4: Since the radial distance 'r' is negative, move in the opposite direction of the angle θ. Instead of plotting the point in the second quadrant, plot it in the fourth quadrant along the same line as θ = 2π/3.
5. Step 5: Mark the point at a distance of 2 units from the origin in the fourth quadrant along the line opposite to θ = 2π/3. This is the correct location of the point (-2, 2π/3) in the polar coordinate system.