A shape is drawn on a centimetre grid. Write down the order of rotational symmetry of the shape.

Answer

The shape drawn on the grid is a rhombus. To determine the order of rotational symmetry, we need to find how many times the shape looks the same as its original position when rotated by 360 degrees. 1. **Initial Position:** The rhombus is in its original orientation. 2. **Rotation by 90 degrees:** If we rotate the rhombus by 90 degrees clockwise or counter-clockwise, it will not look the same as the original shape. The longer diagonal will become horizontal, and the shorter diagonal will become vertical, which changes its appearance relative to the grid. 3. **Rotation by 180 degrees:** If we rotate the rhombus by 180 degrees, it will align with its original appearance. The vertices will be swapped with their opposite vertices, but the overall shape and orientation will be identical to the starting position. 4. **Rotation by 270 degrees:** Similar to 90 degrees, a 270-degree rotation will not make the shape appear the same as the original. 5. **Rotation by 360 degrees:** After a full 360-degree rotation, the shape returns to its exact original position, which is always counted as one instance of symmetry. Therefore, the rhombus looks the same as its original position after a 180-degree rotation and a 360-degree rotation. This means it has an order of rotational symmetry of 2. The order of rotational symmetry of the shape is 2.