To solve this problem, we need to determine which shapes can be formed by reflecting the given shape $X$ over a line.

Step 1: Identifying Possible Reflections

The shape $X$ is an "L" shaped figure. When reflected, there are four possible outcomes depending on the axis of reflection:

1. Horizontal Reflection: Reflect over a horizontal axis.
2. Vertical Reflection: Reflect over a vertical axis.
3. Diagonal Reflection (from top-left to bottom-right).
4. Diagonal Reflection (from top-right to bottom-left).

Step 2: Comparing Each Reflection with the Given Shapes

Let's analyze the shapes in the grid:

• Horizontal reflection of $X$: The horizontal flip of $X$ will result in a shape that looks like the mirror image of $X$ across a horizontal line.
• Vertical reflection of $X$: The vertical flip of $X$ will result in a shape that looks like the mirror image across a vertical line.
• Diagonal reflections: These are more complex and will rotate and reflect the shape simultaneously.

Step 3: Comparing with Shapes A to H

• Shape A: This is a horizontal reflection of $X$, so it's a match.
• Shape B: This shape is not a reflection of $X$, it seems to be rotated.
• Shape C: This shape is a vertical reflection of $X$, so it's a match.
• Shape D: This is neither a reflection nor a rotation of $X$.
• Shape E: This is not a reflection of $X$; it's another rotated version.
• Shape F: This is neither a reflection nor a rotation of $X$.
• Shape G: This is a diagonal reflection of $X$ across the top-right to bottom-left diagonal, so it's a match.
• Shape H: This shape is not a reflection; it looks like another rotation.

Conclusion

The shapes that can be formed by a single reflection of shape $X$ are:

• A, C, and G.

Would you like a more detailed explanation of how reflections work?

Related Questions

1. What is the difference between reflection and rotation in geometric transformations?
2. How do diagonal reflections work on grid-based shapes?
3. Can the shapes in the grid also be formed by rotation instead of reflection?
4. What are the key properties of reflection symmetry in 2D shapes?
5. How can you systematically determine the line of reflection for a given shape?

Tip

When dealing with reflections, always think about where the "mirror" line is. Visualize how each part of the shape moves across the axis!