Discussion
An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72° anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
1. moves forward for 10 cm.
2. turns 144° clockwise.
(A marker shows North up, East right.)
The pattern made by the trace left behind by the ant is
- A.
- B.
- C.
- D.
Answer: C
The trace is the five-pointed star of option (C).
After its first turn the ant heads 72° north of east. It then repeats 'move 10 cm, turn 144° clockwise' five times. Each turn changes its heading by 144°, so after five turns it has turned through 5 × 144° = 720°, exactly two full revolutions, and it is back at P facing its first direction.
A closed path of five equal strokes that turns through two full revolutions is a regular star pentagon. The angle between consecutive strokes at each point is 180° - 144° = 36°, which is the point angle of a five-pointed star.
A regular pentagon (A) would need turns of 72° each, giving one revolution in five steps. A hexagon (B) needs six strokes with 60° turns. The seven-pointed star (D) needs seven strokes, but the ant makes only five.
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