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 by 10 cm.
2. Turns 144º clockwise. The pattern made by the trace left behind by the ant is:
Show Hint
When analyzing movement problems, consider how the combination of rotations and forward movements affects the resulting geometric pattern.
The ant's movement is described in a sequence of turning and moving forward. We need to analyze the pattern formed after five turns.
Step 1: Movement and Turns.
Initially, the ant is facing east. It turns 72º anticlockwise, and then for each of the five steps, it moves forward 10 cm and turns 144º clockwise. The first move will result in the ant facing a new direction, and this continues for the five steps. Each turn creates a geometric pattern, and after five steps, the trace will form a star-like figure.
Step 2: Analyzing the Shape.
Given the specific angles of movement (72º anticlockwise and 144º clockwise), the pattern formed will be symmetric and regular, with all sides equal in length.
Step 3: Conclusion.
Option (C) represents the correct pattern as it correctly matches the symmetrical star shape formed by the ant, with all sides equal to 10 cm.
