The task is to determine which shapes (labeled A to H) can be formed by a single reflection of shape $X$ (the original shape on the left).

Analysis:

A reflection can be done across either a vertical or horizontal axis. Let’s break this down:

1. Original Shape $X$:

   • It is an "L" shape made up of 5 squares.
   • The right side has two squares extending horizontally.
   • There are two main axes we can reflect over:
     • Vertical reflection (over a line going through the middle vertically).
     • Horizontal reflection (over a line going through the middle horizontally).

2. Identifying Reflections:

   • Vertical reflection will flip the two squares that extend horizontally to the left.
   • Horizontal reflection will flip the two squares that extend horizontally downward.

Step-by-Step Evaluation of Shapes A to H:

• Shape A: This is the original $X$ reflected horizontally. Valid reflection.
• Shape B: This shape is similar to $X$ but rotated; it's not a reflection. Not valid.
• Shape C: This shape appears as the result of a vertical reflection of $X$. Valid reflection.
• Shape D: This is neither a horizontal nor vertical reflection of $X$. Not valid.
• Shape E: This appears to be a rotated version of $X$, but it's not a simple reflection. Not valid.
• Shape F: This is a vertically reflected version of $X$. Valid reflection.
• Shape G: This is not a valid reflection of $X$. Not valid.
• Shape H: This is the original $X$ reflected horizontally. Valid reflection.

Conclusion:

The shapes that can be formed by a single reflection of shape $X$ are A, C, F, H.

Let me know if you'd like further details or have any questions!

Related Questions:

1. How would rotating the shape $X$ affect which shapes are formed?
2. Can you explain the difference between rotation and reflection in geometry?
3. What other transformations (besides reflection) could result in shapes like $X$?
4. How do symmetry properties relate to reflections of geometric shapes?
5. Can a combination of reflection and rotation form the other shapes?

Tip: When performing geometric transformations, visualize the axes and how the shape behaves across different reflections or rotations.