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The problem asks for the reflection of the triangle \( \Delta EFG \) across the x-axis. To find the correct reflection, we should flip each vertex of the triangle over the x-axis. The y-coordinate of each point should change its sign (positive to negative or negative to positive), while the x-coordinate remains the same.

### Steps to Reflect the Triangle Across the X-axis:
1. **Identify Coordinates of Points E, F, and G:**  
   Look at the original position of points \( E \), \( F \), and \( G \) from the top graph. Let's denote these points as \( E(x_1, y_1) \), \( F(x_2, y_2) \), and \( G(x_3, y_3) \).

2. **Reflect Each Point Across the X-axis:**  
   For each point, apply the transformation \( (x, y) \to (x, -y) \), flipping the y-coordinate.
   
3. **Select the Correct Graph Based on the Reflected Points:**

- **Option A** reflects the triangle without changing the orientation, but the y-coordinates have flipped.
- **Option B** seems to reflect the triangle correctly, maintaining distances and flipping the triangle properly across the x-axis.
- **Option C** distorts the triangle, making it incorrect.
- **Option D** shows incorrect placement for some vertices.

### Conclusion:
The correct reflection of triangle \( \Delta EFG \) across the x-axis is shown in **Option B**, as it properly flips the triangle without altering its shape.

Would you like more details on how reflections work or have any questions?

Here are 5 related questions you might find useful:
1. How do you reflect a point across the y-axis instead of the x-axis?
2. What happens to the coordinates of a point when reflecting over both the x-axis and y-axis?
3. How do you rotate a triangle 90 degrees around the origin?
4. How does reflecting a shape change its orientation?
5. What is the rule for reflecting over the line \( y = x \)?

**Tip:** Reflections maintain the shape and size of a figure but reverse its orientation depending on the axis used.

Graph the reflection of ΔEFG across the x-axis.

Learn how to graph the reflection of triangle ΔEFG across the x-axis. Understand how to apply coordinate transformations to flip the triangle across the x-axis while maintaining its size and shape. This problem is suitable for students in Grades 6-8.

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