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To rotate the triangle \( \triangle PQR \) counterclockwise by 270° around the origin, we apply the following transformation to each of the points \( P(x_1, y_1) \), \( Q(x_2, y_2) \), and \( R(x_3, y_3) \):

- The rule for a 270° counterclockwise rotation about the origin is \( (x, y) \rightarrow (y, -x) \).

Let's identify the coordinates of points \( P \), \( Q \), and \( R \) from the graph, apply the transformation, and find the new positions.

1. **Identify the coordinates:**
   - \( P \) seems to be at \( (10, 15) \).
   - \( Q \) seems to be at \( (5, 10) \).
   - \( R \) seems to be at \( (10, 0) \).

2. **Apply the 270° rotation rule \( (x, y) \rightarrow (y, -x) \):**
   - For \( P(10, 15) \), the new coordinates will be \( (15, -10) \).
   - For \( Q(5, 10) \), the new coordinates will be \( (10, -5) \).
   - For \( R(10, 0) \), the new coordinates will be \( (0, -10) \).

So, the rotated triangle \( \triangle P'Q'R' \) will have the following coordinates:
- \( P'(15, -10) \),
- \( Q'(10, -5) \),
- \( R'(0, -10) \).

Would you like further clarification on this, or any specific details on how this rotation works? 

Here are some related questions:
1. What are the steps for performing a 90° counterclockwise rotation?
2. How would you rotate a point 180° about the origin?
3. What is the formula for rotating a point clockwise by 270°?
4. How would a reflection across the x-axis affect the points of a triangle?
5. How does a translation differ from a rotation in terms of transformation?

**Tip:** A 270° counterclockwise rotation is the same as a 90° clockwise rotation, which can simplify some problems.

Rotate triangle PQR 270° counterclockwise around the origin.

Learn how to rotate triangle PQR by 270° counterclockwise around the origin on a coordinate plane. This geometry problem involves key concepts such as rotations and the formula (x, y) → (y, -x) for a 270° counterclockwise rotation. Suitable for students in Grades 9-11.

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