Radha moves towards South-East a distance of 7 km, then she moves towards West…

Concept: In direction-sense (distance & direction) problems, resolve every leg of the journey into East-West and North-South components. A diagonal bearing such as South-East or North-West contributes equally to both axes; and two legs that are equal in length but exactly opposite in bearing (South-East vs. North-West) cancel out completely, since their East-West and North-South components are equal in magnitude but opposite in sign.

Application (Radha's path):

1. Take East as the positive x-direction and North as the positive y-direction, with the starting point as the origin (0, 0).

2. She walks 7 km South-East (45° between South and East) — this contributes positively to East and negatively to North.

3. She walks 14 km West — a pure negative x-direction move of 14 km, with no North-South component.

4. She walks 7 km North-West (45° between North and West) — this bearing is exactly opposite to the South-East leg and equal in length (7 km), so its East-West and North-South components are equal in magnitude but reversed in sign from the South-East leg.

5. She walks 4 km East — a pure positive x-direction move of 4 km, with no North-South component.

6. Because the South-East leg and the North-West leg are equal in length and exactly opposite in bearing, their East-West and North-South contributions cancel each other out completely — those two diagonal legs have zero net effect.

7. What remains is only the West leg (14 km) and the East leg (4 km) acting along the same East-West line: net displacement = 14 km West − 4 km East = 10 km West of the start, with zero net North-South displacement.

Cross-check: Since the two diagonal legs are equal in length and directly opposite in bearing, they are equivalent to not moving at all — picture Radha skipping straight from the end of the South-East leg to the end of the North-West leg. What is left is a straight East-West path: 14 km West then 4 km East, net 14 − 4 = 10 km. The diagram below confirms the same result geometrically.

So Radha is 10 km from her starting point.