Megha moves towards the north-west and travels a distance of 10 km. She then…

For a series of straight-line movements, the final displacement from the starting point is the vector sum of all the movements, regardless of the order in which they were made. Whenever two movements are equal in length but exactly opposite in direction, their combined contribution is zero — they cancel out completely.

1. Megha's north-west leg (10 km) and her south-east leg (10 km) are exactly opposite directions of equal length, so together they cancel out and contribute nothing to the final displacement.

2. This leaves only the east leg (15 km) and the west leg (6 km) to determine her position relative to the start.

3. Taking east as the positive direction, the net east-west displacement is 15 km (east) minus 6 km (west), which equals 9 km east of the starting point, since the west leg takes her back part of the way she had gone east.

4. There is no leftover north-south component once the north-west and south-east legs cancel, so her final position lies entirely along the east-west line through the starting point.

As an independent check, resolving every leg into north-south and east-west components confirms the same result: the north-south components of the north-west and south-east legs are equal in size and opposite in sign, so they cancel exactly, while the east-west components combine to the difference between the east and west legs, 15 km minus 6 km, once again giving 9 km. Megha is therefore 9 km from the starting point.