Which image is a result of one reflection over a horizontal line and one 90 degree counter clockwise rotation about any corner of the pattern?

Understand the Problem

The question is asking to identify which transformed image (from options A, B, C, or D) results from reflecting the given quilt pattern over a horizontal line and then rotating it 90 degrees counterclockwise about any of its corners.

Answer

B

Steps to Solve

Reflect the Quilt Pattern Horizontally
Reflect the original quilt pattern over a horizontal line. This means that the top part of the quilt must switch with the bottom part. So, the original pattern:
```
[X X]
[Y Z]
```
after reflection becomes:
```
[Y Z]
[X X]
```
Rotate the Pattern 90 Degrees Counterclockwise
Next, we need to rotate this new pattern 90 degrees counterclockwise about any corner. For the corner in the top left, this transformation changes the order of the squares:
- The square in the top left moves to the top right,
- The square in the bottom left moves to the top left,
- The square in the bottom right moves to the bottom left,
- The square in the top right moves to the bottom right.
The new arrangement after rotation will be:
```
[Z X]
[Y Y]
```
Compare Transformed Image with Options
Now we compare the resulting pattern from the transformation with each of the answer options A, B, C, and D to see which one matches.

The correct answer is B.

More Information

The transformation involves two steps: a reflection and a rotation. Understanding these transformations helps visualize how the quilt pattern moves, ensuring the resulting image matches the transformed pattern.

Tips

Confusing rotation direction: Ensure to remember that "counterclockwise" means moving in the opposite direction of a clock's hands.
Incorrect reflection: Make sure to accurately reflect over the horizontal line by switching top and bottom parts correctly.

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