An insect starts from a point and walks 15 cm towards the East.\nIt then turns to its right and walks 20 cm, turns right again and walks 4 cm, then turns towards the North and walks 20 cm, and finally turns to its left and walks 2 cm.\nWhere is the insect now with respect to its starting point?

Introduction / Context:
This direction sense question describes an insect walking along straight segments with right turns and a specific absolute movement towards the North. We must find the insect's final position relative to its starting point in terms of East–West displacement. The trick is to interpret the sequence of right turns correctly and track horizontal and vertical displacements separately, then compare the final coordinate with the origin.

Given Data / Assumptions:

• The insect starts from an initial point (the origin).
• It walks 15 cm towards the East.
• It then turns to its right and walks 20 cm, which from facing East means walking towards the South.
• Next, it turns right again and walks 4 cm, which from facing South means walking towards the West.
• Then it turns towards the North (absolute direction) and walks 20 cm.
• Finally, it turns to its left and walks 2 cm; from facing North, left indicates the West direction.
• All distances are measured along straight lines and right/left turns are 90 degrees.

Concept / Approach:
We will track the insect's path on a coordinate grid where East–West displacements affect the x-coordinate and North–South displacements affect the y-coordinate. Some segments may cancel the vertical displacement (such as equal South and North movements), leaving only horizontal displacement. At the end, we compare the final coordinates to the origin to see whether the insect is East or West of the starting point and by how much in centimetres.

Step-by-Step Solution:
Step 1: Assume the starting point is (0, 0). Step 2: Walking 15 cm East takes the insect to (15, 0); it is facing East. Step 3: From facing East, a right turn faces South. Walking 20 cm South leads to (15, -20). Step 4: From facing South, a right turn faces West. Walking 4 cm West takes it to (11, -20). Step 5: The insect then turns towards North (absolute direction) and walks 20 cm, moving to (11, 0). The Southward and Northward movements cancel. Step 6: From facing North, a left turn faces West. Walking 2 cm West moves the insect to (9, 0). Step 7: The final position is (9, 0) compared to the starting point (0, 0), so the insect is 9 cm to the East of its starting point.

Verification / Alternative check:
We can sum the horizontal and vertical movements separately. Horizontally, the insect moves 15 cm East, 4 cm West, and 2 cm West. Net horizontal displacement = 15 − 4 − 2 = 9 cm East. Vertically, it moves 20 cm South and 20 cm North, which cancel to zero. Therefore, the insect ends up directly East of the starting point by 9 cm. This matches the coordinate approach and confirms that there is no North–South displacement in the final position.

Why Other Options Are Wrong:
21 cm East or West ignores the net cancellations and overestimates the displacement. 9 cm West would only occur if the Westward movements exceeded the Eastward movement, which is not the case here. 4 cm North assumes there is a net vertical displacement, but the 20 cm South and 20 cm North movements cancel exactly, leaving no net North–South shift. Hence only 9 cm East is consistent with the described path.

Common Pitfalls:
Students may misinterpret the change from relative directions (right/left) to absolute directions (North) and then back to relative directions (left from North), leading to incorrect final directions. Another common error is to add distances without considering direction or to forget to subtract movements in opposite directions. Drawing a simple diagram, marking each turn, and writing cumulative East–West and North–South components is a robust strategy to avoid such mistakes.

Final Answer:
The insect is now located 9 cm East of its starting point.