https://file.aiquickdraw.com/mathbot/file/1727448698616lqnswcs1.jpg

To determine the series of transformations that would map Figure \( P \) onto Figure \( Q \), let's carefully analyze the image. 

### Step-by-step process:

1. **Reflection**:
   - Observing the two figures, it appears that Figure \( Q \) is a reflection of Figure \( P \) over the **x-axis**. All points in Figure \( P \) are mirrored vertically, flipping their y-coordinates.

2. **Translation**:
   - After reflecting, Figure \( P \) still needs to be translated upwards. Specifically, this would be a **vertical translation**. The points of Figure \( P \) are shifted along the y-axis. 

### Transformation steps:
- **Step 1: Reflect** Figure \( P \) across the x-axis. This changes the coordinates of every point from \( (x, y) \) to \( (x, -y) \).
  
- **Step 2: Translate** the reflected figure vertically by **5 units** upwards. This moves the points along the y-axis from \( y' \) to \( y' + 5 \).

With this, Figure \( P \) will align with Figure \( Q \).

Would you like further details on the specific points being transformed, or do you have any questions?

### Related questions:
1. What are the exact coordinates of Figure \( P \) and Figure \( Q \) before and after the transformations?
2. How would the transformation differ if it involved a rotation instead of reflection and translation?
3. Can you identify the line of symmetry after the reflection in this case?
4. How do the orientation and size of Figure \( P \) and Figure \( Q \) compare after the transformations?
5. What would happen if we first translated Figure \( P \) before reflecting it?

### Tip:
When determining transformations, always check for basic operations like reflection, rotation, and translation, and then see how combinations of these might yield the result.

Determine a series of transformations that would map Figure P onto Figure Q.

This geometry problem demonstrates how to map Figure P onto Figure Q using a reflection across the x-axis followed by a vertical translation. Learn how to apply transformations and understand geometric concepts. Suitable for students in Grades 8-10.

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