Total distance moved North = 2 km + 3 km = 5 km. Total distance moved East = 10 km + 2 km = 12 km. The final position forms a right-angled triangle with the starting point. The shortest distance (hypotenuse) is $\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$ km.