The movement forms a right-angled triangle with legs of 4 km east and 3 km north. The straight-line distance from the starting point to the final point is the hypotenuse of this triangle. By the Pythagoras theorem, the hypotenuse is √(4² + 3²) = √(16 + 9) = √25 = 5 km. So the person is 5 km away from the starting point.
Option A:
Option A uses the classic 3–4–5 right-angled triangle pattern, which fits perfectly with the given distances. Applying Pythagoras correctly yields 5 km, making this the exact displacement from the origin.
Option B:
Option B, 6 km, overestimates the distance and would not satisfy the squared relationship 4² + 3² = 5². It suggests a hypotenuse of √36 when the correct sum of squares is 25.
Option C:
Option C, 7 km, exaggerates the distance even more and is not supported by any computed combination of the given legs. It is much larger than the true hypotenuse.
Option D:
Option D, 4 km, simply repeats one leg of the triangle and ignores the northward movement, so it cannot represent the actual straight-line displacement.
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