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is triangle abc a reflection of traingle def across the x axis

To determine if triangle \( \triangle ABC \) is a reflection of triangle \( \triangle DEF \) across the x-axis, we need to compare their corresponding vertices and examine the transformations between them.

### Step-by-Step Analysis:

1. **Identify Coordinates of \( \triangle ABC \):**
   - \( A = (-4, 8) \)
   - \( B = (-2, 6) \)
   - \( C = (-8, 4) \)

2. **Identify Coordinates of \( \triangle DEF \):**
   - \( D = (-4, -6) \)
   - \( E = (-2, -8) \)
   - \( F = (-8, -4) \)

### Reflection Across the x-axis:
When reflecting a point across the x-axis, the x-coordinate stays the same, while the y-coordinate changes its sign (i.e., \( (x, y) \) becomes \( (x, -y) \)).

#### Check the transformation:
- \( A = (-4, 8) \) → Reflection would be \( (-4, -8) \), but the corresponding point \( D = (-4, -6) \), so this is not an exact match.
- \( B = (-2, 6) \) → Reflection would be \( (-2, -6) \), but \( E = (-2, -8) \).
- \( C = (-8, 4) \) → Reflection would be \( (-8, -4) \), and \( F = (-8, -4) \), which matches.

### Conclusion:
The triangles do not appear to be an exact reflection of each other across the x-axis, as only one point matches under reflection, while the others do not.

Would you like to explore this further or have additional details?

### Related Questions:
1. What are the coordinates of triangle \( \triangle LMN \)?
2. Is triangle \( \triangle PQR \) a reflection of any other triangle on the graph?
3. What is the area of triangle \( \triangle ABC \)?
4. Can we identify a transformation that maps \( \triangle ABC \) to \( \triangle DEF \)?
5. How do the side lengths of \( \triangle ABC \) and \( \triangle DEF \) compare?

### Tip:
Always check the coordinates and signs when analyzing transformations like reflections or rotations!

Is triangle ABC a reflection of triangle DEF across the x-axis?

Explore whether triangle ABC is a reflection of triangle DEF across the x-axis by comparing their vertices and transformations. This problem covers key geometric concepts such as reflections and transformations on the coordinate plane. Suitable for students in Grades 8-10.

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