https://file.aiquickdraw.com/mathbot/file/1727184858277kv128q8g.jpg

The image shows a parallelogram \( PQRS \) plotted on a coordinate grid. You are tasked with rotating this parallelogram 90° counterclockwise around the origin.

### To perform a 90° counterclockwise rotation:
For a point \( (x, y) \), the new coordinates after a 90° counterclockwise rotation are given by \( (-y, x) \).

#### Step-by-step process:
1. **Identify the original coordinates** of the points \( P, Q, R, S \):
   - \( P(-8, 2) \)
   - \( Q(-6, 0) \)
   - \( R(-2, 2) \)
   - \( S(-4, 4) \)

2. **Apply the rotation formula** \( (x, y) \rightarrow (-y, x) \):
   - For \( P(-8, 2) \), the new coordinates are \( (-2, -8) \).
   - For \( Q(-6, 0) \), the new coordinates are \( (0, -6) \).
   - For \( R(-2, 2) \), the new coordinates are \( (-2, -2) \).
   - For \( S(-4, 4) \), the new coordinates are \( (-4, -4) \).

3. **Plot the new points** \( P', Q', R', S' \) on the grid:
   - \( P'(-2, -8) \)
   - \( Q'(0, -6) \)
   - \( R'(-2, -2) \)
   - \( S'(-4, -4) \)

After plotting these points, you can connect them to form the rotated parallelogram \( P'Q'R'S' \).

Would you like me to generate a visual of the rotated parallelogram or explain any part further?

Here are some related questions to extend your learning:
1. What is the general rule for rotating a point 180° around the origin?
2. How would you rotate a point 90° clockwise instead of counterclockwise?
3. How can you determine if a shape is symmetric after a rotation?
4. What transformations preserve the area of a shape?
5. How can reflections differ from rotations in their effect on a shape?

**Tip**: Always remember that for a 90° counterclockwise rotation, the rule \( (x, y) \rightarrow (-y, x) \) holds, and for clockwise, it's \( (x, y) \rightarrow (y, -x) \).

Graph the image of parallelogram PQRS after a rotation 90° counterclockwise around the origin.

Learn how to rotate a parallelogram by 90° counterclockwise around the origin using the rotation formula (x, y) → (-y, x). This problem demonstrates how transformations work in coordinate geometry. Suitable for students in Grades 7-10.

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