https://file.aiquickdraw.com/mathbot/file/1729945426580pjusc3bx.jpg

To solve this reflection problem, let's follow these steps:

1. **Identify the vertices of the original triangle**: By examining the image, the vertices of the triangle appear to be:
   - \( A(-6, 1) \)
   - \( B(-4, 4) \)
   - \( C(-2, 1) \)

2. **Reflect each vertex across the x-axis**: Reflection across the x-axis changes the y-coordinate of each point to its opposite sign. So, for each vertex \((x, y)\), the new point will be \((x, -y)\).

   - Reflect \( A(-6, 1) \) to get \( A'(-6, -1) \)
   - Reflect \( B(-4, 4) \) to get \( B'(-4, -4) \)
   - Reflect \( C(-2, 1) \) to get \( C'(-2, -1) \)

3. **Resulting vertices**: The vertices of the reflected triangle are:
   - \( A'(-6, -1) \)
   - \( B'(-4, -4) \)
   - \( C'(-2, -1) \)

Thus, the vertices of the triangle after reflection across the x-axis are:
- \( (-6, -1) \)
- \( (-4, -4) \)
- \( (-2, -1) \)

Would you like further explanation on reflections or transformations?

### Additional Questions
1. How would the reflection change if the triangle were reflected across the y-axis?
2. What are the coordinates if the triangle is reflected across the line \( y = x \)?
3. How would you calculate the reflection if it was across the line \( y = -x \)?
4. How do transformations affect the area of geometric shapes?
5. How would you find the distance between corresponding points of the original and reflected triangles?

### Tip
Remember, reflecting across the x-axis only affects the y-coordinates, while reflecting across the y-axis only affects the x-coordinates.

The triangle is reflected across the x-axis. What are the vertices of the resulting triangle?

Learn how to find the vertices of a triangle after reflecting it across the x-axis. This problem involves understanding geometric transformations, particularly reflections, suitable for students in Grades 6-8.

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