https://file.aiquickdraw.com/mathbot/file/1726767536298kpfdkukx.jpg

We are given a triangle \( \triangle PQR \) on a coordinate grid, and the question asks for the new coordinates of point \( R \) after a **90° counterclockwise rotation** about the origin.

Let's analyze the problem step by step:

1. **Original Coordinates of Point \( R \)**: 
   From the graph, point \( R \) is located at \( (-6, -2) \).

2. **Rotation Rule for 90° Counterclockwise**:
   When a point \( (x, y) \) is rotated 90° counterclockwise about the origin, the new coordinates \( (x', y') \) are given by:
   \[
   (x', y') = (-y, x)
   \]
   So, we switch the coordinates and change the sign of the original y-coordinate.

3. **Applying the Rule**:
   The coordinates of point \( R \) are \( (-6, -2) \). Using the rotation formula:
   \[
   x' = -(-2) = 2 \quad \text{and} \quad y' = -6
   \]
   Thus, the new coordinates of \( R \) after the 90° counterclockwise rotation are \( (2, -6) \).

The correct answer is therefore:
\[
\boxed{(2, -6)}
\]

Would you like further details or have any questions?

Here are 5 questions that expand on this concept:
1. How do you perform a 180° counterclockwise rotation on the same point \( R \)?
2. What happens to a point when rotated 270° counterclockwise about the origin?
3. Can you explain how to rotate a point by 90° clockwise instead?
4. What are the general rules for rotating points by multiples of 90° about the origin?
5. How would the coordinates of point \( P \) change after a 90° counterclockwise rotation?

**Tip**: When rotating points, it's important to remember the direction (clockwise or counterclockwise) as it determines how the coordinates transform!

What are the coordinates of the image of point R after a 90° counterclockwise rotation about the origin?

Explore how to determine the coordinates of point R after a 90° counterclockwise rotation about the origin. The original coordinates of point R are (-6, -2), and after applying the rotation formula, the new coordinates are (2, -6). This solution uses concepts of transformations and rotations in coordinate geometry, suitable for students in Grades 8-10.

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