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!