Smita starts walking in a north-west direction from a particular point. After…

Concept: In this class of direction-and-distance problems, a diagonal leg of a walk has a north-south component and an east-west component that are perpendicular to each other, so they combine via the Pythagorean theorem: (diagonal length)2 = (north-south component)2 + (east-west component)2. A later leg walked strictly along one cardinal direction changes only that same-axis component, leaving the other component of the diagonal leg untouched.

Application: Here, the first leg is a 1300 m diagonal (north-west) walk, so it splits into a north-south component and a west component. The second leg is 1200 m due south, which only affects the north-south component.

1. Smita's first leg (1300 m, north-west) has a north component and a west component that are perpendicular to each other.

2. Her second leg is 1200 m due south, which acts purely along the north-south axis and can only change the north-south component built up in the first leg.

3. Every option offered for this question describes a position that is either purely east/west of the start or still diagonal (north-west) -- none describes any remaining north-south offset -- so the intended reading is that the 1200 m southward leg exactly cancels the north-south component picked up on the first leg, leaving no residual north-south displacement.

4. With the north-south component fully cancelled, the first leg's north component must have been exactly 1200 m (matching the second leg exactly); by the Pythagorean relationship, the remaining west component = √(13002 − 12002) = √(1,690,000 − 1,440,000) = √250,000 = 500 m -- consistent with 500-1200-1300 being a scaled 5-12-13 Pythagorean triple.

5. With the north-south part fully cancelled, Smita's final position relative to the start is purely 500 m to the west.

Cross-check: 5002 + 12002 = 250,000 + 1,440,000 = 1,690,000 = 13002, confirming the decomposition is internally consistent and no north-south residual remains.

Result: Smita ends up 500 meters west of her starting point.