https://file.aiquickdraw.com/mathbot/file/1726616511936wmcckb61.jpg

To solve this problem, we are asked to find the coordinates of the vertices of the shape after a 90° counterclockwise rotation around the origin. In a 90° counterclockwise rotation, the transformation rule is:

\[
(x, y) \rightarrow (-y, x)
\]

This means that for every point on the shape, we swap the coordinates and change the sign of the original y-coordinate.

The coordinates of the points before the rotation (from the image) are:
- \( R(-3, -2) \)
- \( S(-1, -2) \)
- \( T(-1, -8) \)
- \( Q(-3, -8) \)

Now, applying the 90° counterclockwise rotation:

1. For \( R(-3, -2) \), we get \( R' = (2, -3) \)
2. For \( S(-1, -2) \), we get \( S' = (2, -1) \)
3. For \( T(-1, -8) \), we get \( T' = (8, -1) \)
4. For \( Q(-3, -8) \), we get \( Q' = (8, -3) \)

So, the new coordinates after the 90° counterclockwise rotation are:
- \( R' = (2, -3) \)
- \( S' = (2, -1) \)
- \( T' = (8, -1) \)
- \( Q' = (8, -3) \)

Let me know if you need further details or have any questions!

Here are five related questions to practice:
1. What are the coordinates of the point \( (4, 5) \) after a 90° counterclockwise rotation around the origin?
2. What happens to a point under a 180° rotation about the origin?
3. How would you rotate a shape 90° clockwise around the origin?
4. What is the rule for rotating a point 270° counterclockwise around the origin?
5. What is the result of reflecting a point over the x-axis?

**Tip:** For any rotation around the origin, visualize how each axis transforms to make rotations easier!

Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.

Learn how to find the coordinates of points after a 90° counterclockwise rotation around the origin. This problem uses the transformation rule (x, y) → (-y, x). Suitable for students in Grades 8-10.

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