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.
Quadcopter Symmetry E46Aa6
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.