The diagram shows a pattern of shaded squares on a grid of 25 identical squares. Write down the number of lines of symmetry of the pattern and the order of ...

This question tests two separate ideas about the same pattern, so deal with them one at a time.

1. Lines of symmetry. Test each possible mirror line of the \(5\times 5\) grid in turn (the vertical centre line, the horizontal centre line and the two diagonals) and keep only those for which every shaded square is matched by a shaded square in the mirror position. Two of these mirror lines work for this pattern, so it has 2 lines of symmetry [B1].
2. Order of rotational symmetry. Turn the grid about its centre square. A quarter turn of \(90^\circ\) does not reproduce the shading, but a half turn of \(180^\circ\) does, and so does the full turn of \(360^\circ\). That is two matching positions in one revolution, so the pattern has rotational symmetry of order 2 [B1].

The two results agree with a general rule: if a shape has \(n\) lines of symmetry with \(n\ge 1\), its order of rotational symmetry is also \(n\). Here \(n=2\) both times.

A common error is to record order 1 as "no rotational symmetry". Every shape returns to itself after \(360^\circ\), so the smallest possible order is 1, never 0.