A man walks 1 km East, 5 km South, 2 km East, and then 9 km North. How far is he from the starting point now?

Introduction / Context:Add the axis movements and compute the resultant distance using the Pythagorean theorem.

Given Data / Assumptions:

• East: 1 + 2 = 3 km.
• North/South: −5 + 9 = +4 km (net North 4).

Concept / Approach:Resultant vector R = (3, 4) from the origin. Distance is sqrt(3^2 + 4^2).

Step-by-Step Solution:Compute R: (3, 4).Distance = sqrt(9 + 16) = sqrt(25) = 5 km.

Verification / Alternative check:Classic 3-4-5 triangle confirms 5 km.

Why Other Options Are Wrong:3/4/7 km do not equal the computed hypotenuse.

Common Pitfalls:Forgetting to combine the two East legs or mis-signing South/North.

Final Answer:5 KM