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!