The letter $\mathrm{P}$ is written in a $2 \times 2$ grid of squares as shown:

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=136&width=143&top_left_y=165&top_left_x=1311)

A combination of rotations about the centre of the grid and reflections in the two lines through the centre achieves the result:

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=136&width=146&top_left_y=336&top_left_x=1052)

When the same combination of rotations and reflections is applied to | $\mathrm{A}$ |  |
| :--- | :--- |
|  |  | , the result is

(A)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=146&width=152&top_left_y=651&top_left_x=390)
(B)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=140&width=144&top_left_y=651&top_left_x=665)
(C)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=146&width=160&top_left_y=651&top_left_x=928)
(D)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=144&width=138&top_left_y=649&top_left_x=1216)
(E)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-074.jpg?height=141&width=149&top_left_y=653&top_left_x=1473)

## Part C: Each correct answer is worth 8.
One possible way to transform the initial position of the "P" to the final position of the "P" is

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-319.jpg?height=127&width=1692&top_left_y=1904&top_left_x=279)

$90^{\circ}$ counterclockwise about the centre to obtain |  |  |
| :--- | :--- |
|  |  | Applying these transformations to the grid containing the "A", we obtain |  | $A$ |
| :--- | :--- |
|  |  | and then

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-319.jpg?height=138&width=157&top_left_y=2305&top_left_x=282)

. (There are many other possible combinations of transformations which will produce

the same resulting image with the "P"; each of these combinations will produce the same result with the "A".)

Answer: (B)

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