The problem asks us to graph the point on a polar coordinate system with the coordinates $(-3, \frac{\pi}{2})$. Here's how we can determine the correct graph:

Key Steps:

1. Interpret the coordinates:

   • The radius $r = -3$: A negative radius means the point is located in the opposite direction of the angle.
   • The angle $\frac{\pi}{2}$: This angle corresponds to the positive y-axis in standard polar coordinates.

2. Adjust for the negative radius:

   • A negative radius reverses the point to the opposite direction of $\frac{\pi}{2}$, which is $\frac{3\pi}{2}$ (on the negative y-axis).

3. Locate the point on the polar grid:

   • Move 3 units outward in the direction of $\frac{3\pi}{2}$.

Correct Answer:

• The correct graph would place the point 3 units down on the negative y-axis (angle $\frac{3\pi}{2}$). After analyzing the options, Option A is correct.

Would you like a detailed explanation of why the other options are incorrect?

Related Questions:

1. How do you convert polar coordinates to Cartesian coordinates?
2. What happens when the angle in polar coordinates is greater than $2\pi$?
3. How does a negative radius affect the graphing of a polar coordinate?
4. What is the difference between polar and Cartesian coordinates?
5. How can you graph polar equations instead of points?

Tip:

When working with polar coordinates, always check if the radius is negative or the angle exceeds $2\pi$ (or $360^\circ$) for proper placement of the point!