Deepu starts his journey from point A and moves 2 km towards the south. Then he turns to his right and moves 0.5 km. Again he takes a right turn and walks 2 km. Now he takes a left turn and walks 3 km more. How far is he from his starting point A after these movements?

Introduction / Context:
In this direction sense and distance problem, Deepu travels in four legs with right and left turns, some of which have fractional distances. The question asks for his straight line distance from the starting point, not the total path length. It combines understanding of turns with basic coordinate geometry and Pythagoras theorem for distance.

Given Data / Assumptions:

• Deepu starts from point A.
• He walks 2 km south.
• He then turns right from facing south and walks 0.5 km west.
• He again turns right from facing west and walks 2 km north.
• He finally turns left from facing north and walks 3 km west.
• We need the shortest straight line distance from his final position to point A.

Concept / Approach:
We plot the movement on a coordinate plane. Let A be at (0, 0). South reduces the y coordinate, north increases it, east increases the x coordinate, and west reduces it. After computing final coordinates, we compute the straight line distance from the origin using the distance formula derived from Pythagoras theorem: distance = sqrt(x^2 + y^2).

Step-by-Step Solution:
Start at A = (0, 0). Move 2 km south: position becomes (0, -2). Facing south, a right turn leads west, so move 0.5 km west: position becomes (-0.5, -2). Facing west, a right turn leads north, so move 2 km north: position becomes (-0.5, 0). Facing north, a left turn leads west, so move 3 km west: position becomes (-3.5, 0). Final coordinates relative to A are (-3.5, 0). Distance from A = sqrt((-3.5)^2 + 0^2) = 3.5 km.

Verification / Alternative check:
Visually, his vertical movement is 2 km down and 2 km up, cancelling out completely, so he ends on the same east west line as A. Horizontally, he goes 0.5 km west and then 3 km further west, for a total of 3.5 km west of A. Since there is no vertical separation, the straight line distance equals this horizontal distance, 3.5 km.

Why Other Options Are Wrong:
Option B: 2.5 km is less than the total westward displacement.
Option C: 7.5 km is far too large and confuses path length with net displacement.
Option D: 1.5 km underestimates the actual separation.
Option E: None of these is wrong because one of the given values, 3.5 km, exactly matches the computation.

Common Pitfalls:
Students sometimes forget that opposite vertical movements cancel or treat the 0.5 km segment as 5 km due to misreading. Another common mistake is to add all distances to estimate displacement, which is incorrect when path turns are involved. Always separate horizontal and vertical components and then apply the distance formula.

Final Answer:
Deepu is 3.5 km away from his starting point A.