Question

A graph of a polar plane with four points plotted is shown.Four points are plotted on a polar coordinate grid with radial increments of pi over 6 radians. Point A is on the third circle from the pole in the second quadrant at start fraction 2 pi over 3 end fraction radians. Point B is on the third circle from the pole in the first quadrant at start fraction pi over 3 end fraction radians. Point C is on the third circle from the pole in the fourth quadrant at start fraction 5 pi over 3 end fraction radians. Point D is on the third circle from the pole in the third quadrant at start fraction 4 pi over 3 end fraction radians.
Question
Use the image to answer the question.
Match the polar coordinate point left-parenthesis negative 3 comma negative Start Fraction pi over 3 End Fraction right-parenthesis with its correct position on the graph.
(1 point)
Responses

A
A

B
B

C
C

D
D
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Answer 1

To determine the correct position of the polar coordinate point (−3, −π/3) on the polar coordinate grid, we need to interpret the coordinates:

1. The radius (−3) indicates that we move 3 units away from the pole, but in the direction opposite to the angle given.
2. The angle (−π/3) suggests a clockwise rotation from the positive x-axis (the polar axis).

In polar coordinates, a negative radius means to extend in the opposite direction of the angle.

Since −π/3 (which is equivalent to 5π/3 if we add 2π to find the positive angle) corresponds to the fourth quadrant and a radius of 3 means you go 3 units from the pole in that direction, we can look at the plotted points:

- Point C is located at (3, 5π/3), which translates to 3 units in the negative direction of the angle −π/3.

Thus, the point (−3, −π/3) would match with point C.

The answer is:
C