Subjects geometry

Quadcopter Symmetry E46Aa6

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1. **Problem Statement:** A quadcopter has 4 identical arms spaced 90 degrees apart. We need to find the order of rotational symmetry of its body and determine if a 270-degree clockwise rotation changes its appearance from below. 2. **Formula and Concept:** The order of rotational symmetry is the number of times an object looks the same during a full 360-degree rotation. For an object with $n$ identical parts spaced evenly, the order of rotational symmetry is $n$. 3. **Calculate Order of Rotational Symmetry:** Since the quadcopter has 4 identical arms spaced 90 degrees apart, the order of rotational symmetry is: $$\text{Order} = 4$$ This means the quadcopter looks the same after rotations of $90^\circ$, $180^\circ$, $270^\circ$, and $360^\circ$. 4. **Check Appearance After 270-Degree Rotation:** A 270-degree clockwise rotation is one of the symmetry rotations because: $$270^\circ = 3 \times 90^\circ$$ Since the quadcopter looks the same after every 90-degree rotation, it will look unchanged after a 270-degree rotation. 5. **Conclusion:** The order of rotational symmetry is 4, and the quadcopter's shape will appear unchanged to the pilot after a 270-degree clockwise rotation because it matches one of the symmetry rotations.