A shape is drawn on a centimetre grid. [Image of a L-shaped polygon, resembling block letters 'L' or 'T' with a short stem and long base, on a grid.] Write down the order of rotational symmetry of the shape.

Answer

The order of rotational symmetry is the number of times a shape looks exactly the same when rotated 360 degrees around its center. A shape always has at least an order of 1, as it looks the same when rotated by 360 degrees. Let's analyze the given L-shaped figure. Imagine picking a central point within the shape or its bounding box to rotate it. If we rotate this shape by 90 degrees, it will look different. If we rotate it by 180 degrees, it will also look different. Similarly, at 270 degrees, it will be different again. Only when rotated by a full 360 degrees will it return to its original orientation. Since the shape only matches itself once during a 360-degree rotation (at 360 degrees itself), its order of rotational symmetry is 1. Shapes with only an order of rotational symmetry of 1 are sometimes referred to as having no rotational symmetry, other than trivial symmetry.