The question involves a regular pentagon with rotational symmetry and asks for the location of point E under the third order of symmetry. Let’s solve this step by step:

Symmetry Explanation:

1. A regular pentagon has rotational symmetry of order 5, meaning it can be rotated $72^\circ$ multiple times and still look the same.
   $360^\circ / 5 = 72^\circ$
2. The third order of symmetry means rotating the pentagon $3 \times 72^\circ = 216^\circ$ clockwise.

Steps to Find E’s New Position:

• Initially, the vertices are labeled as A, B, C, D, E in a clockwise manner.
• Rotating $216^\circ$ clockwise:
  • Point $A$ moves to $D$,
  • Point $B$ moves to $E$,
  • Point $C$ moves to $A$,
  • Point $D$ moves to $B$,
  • Point $E$ moves to $C$.

Final Answer:

Under the third order of symmetry, point $E$ moves to the position of point $C$.

Would you like me to explain this concept further or provide a visualization? Let me know!

Related Questions:

1. What is the definition of rotational symmetry for polygons?
2. How do you calculate the angle of rotation for any regular polygon?
3. How many symmetry orders does a regular pentagon have?
4. What happens to other points under the first and second orders of symmetry?
5. Can rotational symmetry apply to irregular shapes?

Tip:

A regular $n$-sided polygon always has rotational symmetry of order $n$, where each rotation equals $\frac{360^\circ}{n}$.