The image shows a geometry question about reflections over the x-axis. The pre-image of a quadrilateral, labeled as $D, E, F, G$, is shown in the top grid. You are asked to identify which of the figures represents the reflection of this shape over the x-axis.

When reflecting a figure over the x-axis, each point's y-coordinate changes sign while the x-coordinate stays the same. For example, a point $(x, y)$ would reflect to $(x, -y)$.

Let's analyze the provided options:

• The first option shows a triangle with points labeled $D', E', G'$. This seems to be a correct reflection, as the y-coordinates of the points are negative versions of the original coordinates.
• The second option is another reflection, but it is a smaller shape and doesn't match the transformation we're expecting.
• The third option shows the reflected shape, but it is rotated incorrectly.

Based on the above analysis, the correct reflection is represented by the first option.

Would you like further clarification or to discuss reflections in more detail?

Related questions:

1. How does the x-axis reflection affect the coordinates of a point?
2. What would happen if you reflected the shape over the y-axis instead?
3. How do you graphically show reflections of other geometric shapes (e.g., circles, lines)?
4. How would the reflection change if the figure were rotated first?
5. Can you identify the effects of combining reflections with translations?

Tip:

When performing a reflection over the x-axis, simply negate the y-coordinate of each point. This makes it easier to plot reflected images on the coordinate plane.