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

Answer

The problem asks to determine the order of rotational symmetry of the given shape. The shape resembles the letter 'T' if rotated. Rotational symmetry is when a shape looks the same after being rotated a certain number of degrees around a central point. The order of rotational symmetry is the number of times the shape looks the same in one full rotation (360 degrees). Let's analyze the given shape: 1. **Original Position:** The shape is initially oriented with its long vertical bar at the left and a shorter horizontal bar extending to the right from the top of the vertical bar. 2. **Rotation by 90 degrees clockwise:** If we rotate the shape 90 degrees clockwise, the long bar would be horizontal at the top, and the shorter bar would extend downwards from its right end. This is not the original orientation. 3. **Rotation by 180 degrees clockwise:** If we rotate the shape 180 degrees clockwise, the long bar would be at the right, and the shorter bar would extend to the left from the bottom of the long bar. This is not the original orientation. 4. **Rotation by 270 degrees clockwise:** If we rotate the shape 270 degrees clockwise, the long bar would be horizontal at the bottom, and the shorter bar would extend upwards from its left end. This is not the original orientation. 5. **Rotation by 360 degrees clockwise:** After a full 360-degree rotation, the shape will return to its original position. Every shape has at least an order of rotational symmetry of 1 (a 360-degree rotation). Let's carefully re-examine the shape for any other symmetries. The shape is an 'L' shape and then another rectangle attached. It is not a standard geometric shape like a square, rectangle, or circle that might have higher orders of rotational symmetry. Consider the center of the shape. If we rotate it around its perceived center, for the shape to look identical, every part of it must align perfectly with its original position. The given shape: ``` _ _ _ | | | ___ | | | _ ``` (This is a rough ASCII representation of the shape. Imagine a vertical bar, and at its top-right, a horizontal bar extends, then a short vertical bar goes down, then another horizontal bar extends to the left, and a final short vertical bar completes the 'L' shape with an extended top right part.) Let's visualize the shape on the grid. It starts at (2,6) as the bottom-left corner of the first vertical segment. It goes up to (2,9). From (2,9), it goes right to (4,9). From (4,9), it goes down to (4,8). From (4,8), it goes left to (3,8). From (3,8), it goes down to (3,6). From (3,6), it goes left to (2,6). This shape is an irregular polygon. To have rotational symmetry of order greater than 1, there must be an angle of rotation less than 360 degrees (e.g., 180 degrees, 90 degrees) where the shape maps onto itself. Let's try rotating it 180 degrees. If we rotate this shape 180 degrees, the 'L' part will be inverted, and the extended part will also be inverted relative to its original position. The shape will not look the same. For example, the "foot" of the L-shape (the bottom horizontal part) is 1 unit wide. The top horizontal part that extends to the right is 2 units long. If rotated 180 degrees, the bottom part would become the top, etc., and the asymmetry of the 'T' or 'L' shape would become very apparent. Therefore, the only rotation that makes the shape look exactly the same is a full 360-degree rotation. The order of rotational symmetry is the number of times a figure can be rotated about its center such that it looks identical to its original position within a 360-degree rotation. Since the shape only looks identical after a 360-degree rotation, its order of rotational symmetry is 1. Final Answer is 1.