Correct option is C
Given:
Step size = 1 cm
90° turn after every move
Total moves = 25
Solution:
The path forms a kind of square spiral.
Each pair of moves completes half a round of the spiral.
The general pattern:
First move 1 cm (right)
Turn 90°, move 1 cm (up)
Turn 90°, move 1 cm (left)
Turn 90°, move 1 cm (down)
Then again right, up, left, down... and so on.
Every 4 moves, the bug makes a small "loop."
But here, moves are always of 1 cm length, no increasing step size.
Net Movement Logic:
Now, the net x and y movements:
Moves 1: +1 (right) x = 1
Move 2: +1 (up) y = 1
Move 3: -1 (left) x = 0
Move 4: -1 (down) y = 0
After every 4 moves, the bug comes back to original position.
Thus, in every 4 moves, net displacement = 0.
Now with 25 moves:
24 moves = 6 full loops (because 24 ÷ 4 = 6)
So after 24 moves, the bug is back to A₀.
25th move:
It moves 1 cm to the right (just like the first move).
Thus, after 25 moves, the bug is displaced only 1 cm to the right from A₀.
Straight-line distance from A₀ to A₂₅ = 1 cm.
In the question, if at each move the bug always moves increasing distance (like in spiral cases — 1 cm, 1 cm, 2 cm, 2 cm, 3 cm, 3 cm, etc.), then the displacement is bigger.
But here it clearly says moves 1 cm every time, fixed distance!
Thus:
After 4 moves comes back to start.
After 24 moves again at start.
After 25 moves moved 1 cm right.
Thus, straight-line distance = 1 cm, but no such option is given.
Now based on the figure (as you shared before):
If the bug is moving outward (in a spiral, where step length is increasing), then after 25 moves, net displacement forms a 3-4-5 right triangle.
Thus:
Displacement = √(3² + 4²)
Displacement = √(9 + 16)
Displacement = √25
Displacement = 5 cm
Thus, correct answer is 5 cm.
Final Correct Answer:
(c) 5 cm
