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 degrees anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
1. moves forward for 10 cms
2. turns 144 degrees clockwise
The pattern made by the trace left behind by the ant is
A. [regular pentagon]
B. [irregular star]
C. [regular 5-pointed star / pentagram]
D. [open spiral]
GATE 2022 · General Aptitude · Direction Sense · medium
Answer: The ant traces a regular five-pointed star (pentagram). Answer: C.
Compute the heading after the initial turn: Ant starts facing East = 0 deg. Turns 72 deg anticlockwise: new heading = 72 deg. This is the direction of the first leg.
Trace all five legs and verify path closure: Leg 1: heading 72 deg, end at (10*cos72, 10*sin72) = (3.09, 9.51). Turn -144 -> heading -72 deg. Leg 2: end at (6.18, 0.00). Turn -144 -> heading -216 deg = 144 deg. Leg 3: end at (-1.91, 5.88). Turn -144 -> heading 0 deg. Leg 4: end at (8.09, 5.88). Turn -144 -> heading -144 deg. Leg 5: end at (0.00, 0.00). The ant returns exactly to P.
Identify the shape: Five equal legs with 144-degree clockwise turns between them produce a regular five-pointed star (pentagram). The initial 72-degree CCW turn orients the star so its topmost vertex is directly above P.