A man starts walking in the north-easterly direction from a particular point. After walking a distance of 500 metres, he turns southward and walks a distance of 400 metres. At the end of this walk he is situated

Treat the 500 m “north‑easterly” displacement as resolved into perpendicular east and north components using the 3–4–5 Pythagorean triple scaled to 500 m: 300 m east and 400 m north. After the subsequent 400 m due south, the north component becomes 400 − 400 = 0 while the east component remains 300 m. Hence his final position is 300 metres east of the starting point. This decomposition and final coordinate are the same as given in the provided solution snippet, which records the final position as (300 m East, 0 m North).