Complete the table :
`{:("Point","Transformation ","Image"),((4,-8), .....................,(-4,-8)):}`

Answer

To complete the table with the given point and its image, we need to analyze the transformation that occurs between the point and its image.

### Step-by-Step Solution:

1. **Identify the Given Point and Image:**
- The point is \( P(4, -8) \).
- The image is \( P'(-4, -8) \).

2. **Determine the Coordinates:**
- The coordinates of the point \( P \) are \( (4, -8) \).
- The coordinates of the image \( P' \) are \( (-4, -8) \).

3. **Analyze the Transformation:**
- We notice that the y-coordinate remains the same: \( -8 \).
- The x-coordinate changes from \( 4 \) to \( -4 \), indicating a sign change.

4. **Identify the Axis of Reflection:**
- Since the y-coordinate does not change and the x-coordinate changes sign, the transformation is a reflection across the y-axis.
- The reflection of a point \( (x, y) \) across the y-axis is given by the formula \( (-x, y) \).

5. **Complete the Table:**
- Now we can fill in the table:
- Point: \( (4, -8) \)
- Transformation: Reflection in the y-axis
- Image: \( (-4, -8) \)

### Final Table Entry:
- Point: \( (4, -8) \)
- Transformation: Reflection in the y-axis
- Image: \( (-4, -8) \)