Let the starting point be at the origin (0, 0).
After moving 15 km East, Rekha is at position (15, 0).
After turning North and moving 4 km, Rekha is at position (15, 4).
After turning West and traveling 12 km, Rekha is at position:
(15−12,4)=(3,4)
The distance from the starting point (0, 0) to final position (3, 4) is:
d=(3−0)2+(4−0)2
d=9+16
d=25
d=5 km
The final position is (3, 4), meaning Rekha is 3 km to the East and 4 km to the North of her starting point.
Therefore, she is in the North-East direction.
Rekha is 5 km away from her starting point in the North-East direction.
The answer is Option 2: 5 km, North-East.