The answer is: distance is 3 km, displacement is 2.24 km.
Distance is total length: 1 km east + 1 km south + 1 km east again = 3 km
Displacement is the hypotenuse of the right triangles which sides are 1 km east and 2 km south. According to the Pythagorean theorem:
a² + b² = c²
1² + 2² = c²
1 + 4 = c²
5 = c²
c = √5
c = 2.24 km