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To solve the problem of rotating the point \((-2, -3)\) 90 degrees counterclockwise around the origin \((0, 0)\), we can use the following rotation formula for a 90° counterclockwise rotation:

\[
(x', y') = (-y, x)
\]

Given the point \((-2, -3)\):
- The \(x\)-coordinate is \(-2\) and the \(y\)-coordinate is \(-3\).
- After applying the formula:
  - The new \(x'\)-coordinate becomes \(-(-3) = 3\),
  - The new \(y'\)-coordinate becomes \(-2\).

Thus, the rotated point is \((3, -2)\).

The correct answer is **C: (3, -2)**.

Would you like further details or have any questions? 

Here are 5 related questions to expand on this concept:
1. What is the formula for rotating a point 180 degrees about the origin?
2. How would the coordinates change if the point was rotated 90 degrees clockwise instead?
3. Can you describe how rotation transformations preserve distances and angles?
4. How can you use matrices to represent and compute rotations?
5. What happens to a point if it's rotated by 360 degrees?

**Tip:** When rotating a point, the sign changes based on the direction and angle of rotation. Understanding the formula helps to predict these changes accurately.

The point (-2, -3) is rotated 90 degrees counterclockwise using center (0, 0). What are the coordinates of the image?

Learn how to rotate the point (-2, -3) by 90 degrees counterclockwise about the origin (0, 0) with a step-by-step solution. This problem involves the rotation formula (x', y') = (-y, x) and is suitable for students in Grades 8-10.

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