The problem involves analyzing the given transformations of rectangle $WXYZ$ to determine which graphs represent a valid rigid transformation. A rigid transformation preserves the shape and size of the figure, meaning the distances between corresponding points remain the same, and angles are unchanged.

Steps to Analyze:

1. Original Coordinates: From the provided graph of rectangle $WXYZ$:

   • $W(3, 6)$
   • $X(3, 2)$
   • $Y(0, 2)$
   • $Z(0, 6)$

2. Rigid Transformations: Types of rigid transformations include translations, reflections, and rotations. These do not change the size or shape of the rectangle.

3. Verification: Each of the answer options needs to be checked for:

   • Preservation of side lengths: The transformed rectangle must have the same dimensions as the original.
   • Correct correspondence: Verify each vertex is mapped correctly.

Observations from the Images:

• First Option (Top Left): This appears to be a translation of the original rectangle downward and slightly to the right. All side lengths and orientation are preserved. Valid.
• Second Option (Top Right): This shows a reflection across the $y$-axis. The orientation is flipped, but distances and angles are preserved. Valid.
• Third Option (Bottom Left): This is another rigid transformation, likely a 90° clockwise rotation around a point. Dimensions are preserved. Valid.
• Fourth Option (Bottom Right): This seems to show an incorrect transformation where distances are not preserved, as the rectangle looks stretched or distorted. Not valid.

Final Answer:

The valid transformations are Top Left, Top Right, and Bottom Left.

Would you like further clarification or details about this process?

Here are 5 related questions to deepen your understanding:

1. How can you mathematically confirm if a transformation is rigid using distance formulas?
2. What are examples of non-rigid transformations?
3. How does rotation affect the orientation of shapes on a coordinate plane?
4. Can reflections across axes be combined into a single transformation?
5. What are practical uses of rigid transformations in geometry?

Tip: When analyzing transformations, always check the distances between key points to ensure the transformation preserves the shape and size of the figure!