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!