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GATE 2022 CE (CE2) – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

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 72o 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 144o clockwise. The pattern made by the trace left behind by the ant is

Four labelled path choices: regular pentagon, regular hexagon, five-pointed star and seven-pointed star, each with 10 cm walking segments. See the attached source image.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Correct answer: (C) Option C in the figure

Explanation

The five successive walking directions are 72°, −72°, −216°, −360° and −504° relative to east. The 144° turn skips a vertex of a regular pentagon on each segment.

Five equal segments close into a five-pointed star, matching **C**. The final turn changes orientation but adds no trace.