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.