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The task involves mapping triangle \( \Delta EFG \) to its reflection, triangle \( \Delta E'F'G' \), and completing the coordinates of points \( E' \), \( F' \), and \( G' \).

### Analyzing the Reflection:
The reflection appears to be across the **x-axis**, based on the positioning of the original triangle \( \Delta EFG \) and its reflected image \( \Delta E'F'G' \).

For a reflection across the x-axis, the coordinates of any point \( (x, y) \) change to \( (x, -y) \). This transformation applies to all the vertices \( E \), \( F \), and \( G \).

### Step-by-Step Reflection:
- \( E(-3, 5) \) reflects to \( E'(-3, -5) \).
- \( F(-2, 2) \) reflects to \( F'(-2, -2) \).
- \( G(-4, 2) \) reflects to \( G'(-4, -2) \).

### Completing the Table:
\[
\begin{array}{|c|c|}
\hline
\Delta EFG & \Delta E'F'G' \\
\hline
E(-3, 5) & E'(-3, -5) \\
F(-2, 2) & F'(-2, -2) \\
G(-4, 2) & G'(-4, -2) \\
\hline
\end{array}
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the general rule for reflecting a point across the y-axis?
2. How would the reflection change if the triangle were reflected across the y-axis instead?
3. What happens to the coordinates of a point when reflected across the line \( y = x \)?
4. Can you determine the distance between the original points and their reflections?
5. How can you verify if two triangles are congruent after a reflection?

### Tip:
Always remember that reflecting a point across the x-axis only changes the sign of the y-coordinate.

Show how each vertex of ΔEFG maps to its image. Describe in words how to map ΔEFG to its image ΔE'F'G' using a reflection. Complete the table with the coordinates of the image points E', F', and G'.

Learn how to reflect triangle ΔEFG across the x-axis, mapping its vertices E, F, and G to E', F', and G'. This geometry problem involves understanding reflections and transformations on the coordinate plane. Suitable for students in Grades 6-8.

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