The figure below is made up of identical squares. Shade three more squares to form a symmetric figure with XY as the line of symmetry.

1. Identify the line of symmetry and the rule for reflection.

The line of symmetry $XY$ is the diagonal from the bottom-left to the top-right. In a coordinate system where $(c, r)$ represents column $c$ and row $r$, the line of symmetry is $c = r$. The reflection of any square $(c, r)$ across this diagonal is $(r, c)$.

2. Find the reflections of the currently shaded squares.

We check the reflection of each shaded square:

• $(4, 6) \rightarrow (6, 4)$ (Row 4, Col 6) - currently unshaded
• $(2, 5) \rightarrow (5, 2)$ - already shaded
• $(5, 5) \rightarrow (5, 5)$ - on the line of symmetry
• $(3, 4) \rightarrow (4, 3)$ - already shaded
• $(4, 4) \rightarrow (4, 4)$ - on the line of symmetry
• $(5, 3) \rightarrow (3, 5)$ (Row 5, Col 3) - currently unshaded
• $(5, 1) \rightarrow (1, 5)$ (Row 5, Col 1) - currently unshaded

3. Identify the three squares to be shaded.

The three unshaded squares that need to be shaded to complete the symmetry are $(1, 5)$, $(3, 5)$, and $(6, 4)$.