https://file.aiquickdraw.com/mathbot/file/1726231199311qfodqzlh.jpg

To solve this problem, we need to describe the single transformation that takes shape \( P \) to shape \( Q \).

### Observations:
1. **Shape P** is a small triangle located in the bottom left quadrant of the grid.
2. **Shape Q** is a larger triangle in the center of the grid.
3. The triangles are similar in shape but differ in size, indicating an **enlargement**.

### Transformation Description:
The transformation that takes shape \( P \) to shape \( Q \) is an **enlargement**.

To fully describe this enlargement:
- We need to identify the **scale factor** and the **center of enlargement**.

#### Step 1: Find the Scale Factor
- Measure the lengths of corresponding sides of shapes \( P \) and \( Q \).
- Let's say one side of shape \( P \) (the base) is 2 units and the corresponding side of shape \( Q \) is 6 units.
- The scale factor is calculated as:
  \[
  \text{Scale factor} = \frac{\text{Side length of } Q}{\text{Side length of } P} = \frac{6}{2} = 3
  \]

#### Step 2: Identify the Center of Enlargement
- The center of enlargement is the point from which all points of shape \( P \) are enlarged by the scale factor to get shape \( Q \).
- To find the center, draw lines through corresponding points of \( P \) and \( Q \). The point where all these lines intersect is the center of enlargement.
  
Upon inspection of the grid, it appears that the center of enlargement is at point \((2, 2)\).

### Final Answer:
The single transformation that takes shape \( P \) to shape \( Q \) is an **enlargement** with a scale factor of 3 and a center of enlargement at point \((2, 2)\).

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you determine the center of enlargement without a grid?
2. What happens if the scale factor is less than 1?
3. Can a transformation be a combination of two different types?
4. How can you describe a reflection transformation?
5. What is the difference between rotation and enlargement?

**Tip:** Always check the orientation of the shapes to ensure the correct transformation type!

Describe fully the single transformation that takes shape P to shape Q.

Learn how to describe the single transformation from shape P to shape Q using enlargement. This problem involves finding the scale factor and the center of enlargement. Suitable for students in Grades 8-10.

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