https://file.aiquickdraw.com/mathbot/file/1730519205409gkeaqiav.jpg

To map shape \( P \) onto shape \( Q \), we need to identify the transformation that takes one triangle to the other.

### Analysis
1. **Observation of Size and Orientation**:
   - Shape \( Q \) is a larger triangle than \( P \).
   - Both triangles share the same orientation, so this suggests a transformation involving enlargement without rotation.

2. **Scale Factor**:
   - Shape \( Q \) is exactly twice the size of shape \( P \). This indicates an enlargement with a scale factor of \( 2 \).

3. **Center of Enlargement**:
   - We need to find the center of enlargement. By drawing lines from corresponding vertices of \( P \) and \( Q \), they intersect at point \( (3, 2) \).

### Conclusion
The single transformation that maps shape \( P \) onto shape \( Q \) is an **enlargement with a scale factor of \( 2 \) centered at \( (3, 2) \)**.

Would you like further details or have any questions?

### Related Questions
1. How would the transformation change if the scale factor were negative?
2. What other types of transformations could map one triangle onto another?
3. How can you determine the center of enlargement using only coordinates?
4. If the scale factor were \( \frac{1}{2} \), where would the new triangle be located?
5. How does the orientation of a shape affect possible transformations?

### Tip
When identifying an enlargement, always check for the center by connecting corresponding vertices and observing their intersection point.

Describe fully the single transformation that maps shape P onto shape Q.

Learn how to describe the transformation that maps shape P onto shape Q. This problem involves concepts of enlargement with a specific scale factor and center, relevant to geometry transformations. Suitable for students in Grades 8-10.

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