A woman walks 13 km West, then turns South and walks 5 km, then turns East and…

Concept: In direction-tracing problems, treat East-West as one axis and North-South as the other, and track the walker's displacement leg by leg on these axes. A right turn rotates the current heading 90° clockwise following the compass order North → East → South → West → North, while a left turn rotates it 90° the other way.

1. Starting at the initial position, she walks 13 km West — displacement so far: 13 km West, 0 km on the North-South axis.

2. She turns South and walks 5 km — this adds 5 km to the southward displacement while the East-West figure stays at 13 km West.

3. She turns East and walks 13 km — walking East by the same 13 km exactly cancels the earlier westward leg, so the East-West displacement returns to 0; she is now facing East.

4. She turns right while facing East: applying the clockwise rule (North → East → South → West), a right turn from East faces South. Walking 2 km on this heading adds to the southward displacement already covered.

Cross-check: Sum each axis independently. East-West legs: 13 km West and 13 km East cancel to 0. North-South legs: 5 km + 2 km = 7 km, both accumulated in the same southbound rotational sense established when she turned South in leg 2 and again turned right (South) from East in leg 4.

With a 0 km East-West offset and 7 km accumulated southward, her final position is 7 km South of her initial position.