https://file.aiquickdraw.com/mathbot/file/1727461577428l9rjzmo9.jpg

Let's start by analyzing the image and solving the given problem.

The coordinates of point **P** on the grid appear to be approximately **(4, 4)**.

### Part (a)
You are asked to find the coordinates of point **P** after:
1. A reflection in the **x-axis**.
2. A reflection in the **y-axis**.

For reflections:
- Reflecting across the **x-axis** changes the sign of the **y-coordinate**.
- Reflecting across the **y-axis** changes the sign of the **x-coordinate**.

1. **Reflection in the x-axis:**
   - The x-coordinate remains the same.
   - The y-coordinate becomes the negative of the original value.
   - **New coordinates**: (4, -4)

2. **Reflection in the y-axis:**
   - The y-coordinate remains the same.
   - The x-coordinate becomes the negative of the original value.
   - **New coordinates**: (-4, 4)

### Sentence to explain how the answers relate to the coordinates of P:
- "When reflecting point P across the x-axis, only the y-coordinate changes sign. Similarly, when reflecting P across the y-axis, only the x-coordinate changes sign."

### Part (b)
You are asked to find the coordinates of point **P** after:
- A reflection in the **x-axis**, followed by
- A reflection in the **y-axis**.

This can be done step by step:
1. First, reflect **P** (4, 4) in the **x-axis**: The result is **(4, -4)**.
2. Now, reflect the result **(4, -4)** in the **y-axis**: The new coordinates will be **(-4, -4)**.

Thus, after both reflections, the coordinates of point **P** are **(-4, -4)**.

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Would you like further clarification or more details?

Here are five follow-up questions you could explore:
1. What happens if you reflect a point over both the x-axis and y-axis simultaneously?
2. How would the result change if you reflected across the line \(y = x\) instead of an axis?
3. Can you find the result of reflecting point \( P(4, 4) \) over the origin?
4. How does the process of reflection differ in three-dimensional space?
5. What are the coordinates after a reflection in the line \(y = -x\)?

**Tip:** When performing reflections, always note which axis or line the reflection is performed across to correctly adjust the coordinates.

a) Work out the coordinates that the point P maps to after a single reflection in: i) the x-axis, ii) the y-axis. b) Work out the coordinates that P maps to after a reflection in the x-axis and then a reflection in the y-axis.

This problem helps students understand how to reflect a point across the x-axis and y-axis. By applying the reflection rules, you will find the new coordinates of point P after reflections, step by step.

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