In the diagram, which of the following squares should be shaded to make $B D$ a line of symmetry of square $A B C D$ ?
(A) $P$ and $S$
(B) $Q$ and $S$
(C) $P$ and $T$
(D) $Q$ and $T$
(E) $P$ and $R$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-017.jpg?height=282&width=290&top_left_y=1423&top_left_x=1422)
For $B D$ to be a line of symmetry of $A B C D$, the squares labelled $P$ and $S$ should be shaded.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-069.jpg?height=285&width=288&top_left_y=931&top_left_x=1016)

To see why this is, consider that the reflection in $B D$ of vertex $A$ is vertex $C$, and so the reflection in $B D$ of side $D A$ is side $D C$.

Further, the reflection in $B D$ of the first column of square $A B C D$ is the first row of square $A B C D$.

Thus, the reflection in $B D$ of the shaded square in row 3 , column 1 is the square in row 1 , column 3 (the square labelled $P$ ).

More generally, the reflection in $B D$ of the square in row $r$, column $c$ is the square in row $c$, column $r$.

Thus, the reflection in $B D$ of the shaded square in row 5 , column 2 is the square in row 2 , column 5 (the square labelled $S$ ).

ANSWER: (A)