To determine the position of point \( A \) after a \( 240^\circ \) rotation about the center of the regular hexagon \( ABCDEF \), we need to understand the geometric properties of regular hexagons and rotations.
A regular hexagon is a six-sided polygon with all sides and angles equal. Let's label the vertices in a clockwise manner as \( A, B, C, D, E, F \).
A \( 240^\circ \) rotation about the center of the hexagon moves any point \( \frac{240^\circ}{360^\circ} \times 6 = 4 \) positions in the clockwise direction (since \( \frac{360^\circ}{6} = 60^\circ \) per step).
Since we are starting with point \( A \), we will apply the \( 240^\circ \) rotation and count four positions clockwise:
- Starting at \( A \):
1. First position: \( F \)
2. Second position: \( E \)
3. Third position: \( D \)
4. Fourth position: \( C \)
Therefore, after a \( 240^\circ \) rotation about the center, point \( A \) will land on point \( C \).
9. ABCDEF is a regular hexagon. What point will A land on after a 240o rotation about the center?
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