Final answer:
The boy's resultant displacement is calculated using the Pythagorean theorem, which results in a magnitude of 5 km northeast.
Step-by-step explanation:
To find the magnitude of his resultant displacement, we can use the Pythagorean theorem since the movements east and north are at right angles to each other. We calculate the resultant displacement by taking the square root of the sum of the squares of the individual displacements.
Displacement magnitude = √(east displacement² + north displacement²).
Substituting the given values, we get:
Displacement magnitude = √(3.0 km² + 4.0 km²) = √(9 + 16) km² = √25 km² = 5 km.
Therefore, the resultant displacement is 5 km northeast.