Determine Whether Each Of The Figures Below Has Rotational Symmetry. If So, Find The Rotation In Degrees About The Center That Maps The Figure Onto Itself. 2. 3. 4.
The Correct Answer and Explanation is:
To accurately determine whether figures 2, 3, and 4 have rotational symmetry and identify their corresponding angles of rotation, I would need to see the figures you are referring to. Please upload or describe the figures labeled 2, 3, and 4.
However, I can provide a general explanation of how to determine rotational symmetry and how the angle is calculated. Once you provide the figures, I can apply this method to each.
General Explanation
Rotational symmetry occurs when a figure can be rotated (less than 360°) about a central point and still look exactly the same as it did before the rotation. In such cases, the shape “maps onto itself” during the rotation. The number of times a shape maps onto itself in a full 360° rotation determines the order of rotational symmetry, and the smallest positive angle for which this occurs is called the angle of rotation.
To determine if a shape has rotational symmetry:
- Identify the center of the figure – typically the geometric center.
- Rotate the figure around the center by various angles (like 90°, 120°, 180°, etc.).
- Check if the figure looks the same after rotation.
Common examples:
- A square has rotational symmetry of order 4 because it maps onto itself at 90°, 180°, 270°, and 360°. Its angle of rotation is 90°.
- An equilateral triangle has order 3 and an angle of rotation of 120°.
- A regular hexagon has order 6 and an angle of 60°.
- A rectangle (non-square) has rotational symmetry of order 2 with a 180° rotation.
- An irregular shape, such as an L-shape or scalene triangle, typically has no rotational symmetry.
To find the angle of rotation for a shape with symmetry, divide 360° by the number of times it maps onto itself: Angle of Rotation=360∘Order of Symmetry\text{Angle of Rotation} = \frac{360^\circ}{\text{Order of Symmetry}}
