https://file.aiquickdraw.com/mathbot/file/17268029883510b27j05q.jpg

The problem shown in the image asks to **rotate triangle \( \triangle PQR \) by 270° counterclockwise around the origin**. Let's break down how to approach this type of transformation:

1. **Rotation of points 270° counterclockwise**:
   - The general rule for a 270° counterclockwise rotation around the origin is to switch the coordinates of each point and negate the new first coordinate.
   - For a point \( (x, y) \), the transformation is:
     \[
     (x, y) \rightarrow (y, -x)
     \]

2. **Applying the rule to each vertex of the triangle**:
   - Assume the coordinates of \( P \), \( Q \), and \( R \) are \( P(x_1, y_1) \), \( Q(x_2, y_2) \), and \( R(x_3, y_3) \). Based on the diagram, these points will be rotated using the rule \( (x, y) \rightarrow (y, -x) \).
   - After the transformation, the new coordinates of \( P' \), \( Q' \), and \( R' \) will be plotted on the graph.

Would you like me to calculate the new coordinates of the points \( P \), \( Q \), and \( R \) from the diagram? Let me know if you need more details on any specific part of the process!

### Further Questions to Explore:
1. What is the rule for a 90° counterclockwise rotation around the origin?
2. How does the rotation affect the orientation of the shape?
3. What happens to a shape's size and angles during rotation?
4. How can you verify the accuracy of a transformation on a graph?
5. How does the triangle's image differ after a reflection instead of a rotation?

**Tip:** Always remember the origin is the fixed point during any rotation unless stated otherwise.

Rotate ∆PQR 270° counterclockwise around the origin.

Learn how to rotate triangle ∆PQR 270° counterclockwise around the origin. This problem involves key concepts of geometry, coordinate transformations, and rotation formulas. Suitable for students in Grades 7-9.

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