Final answer:
Alan covered a total distance of 2600 km on his journey. However, his displacement is 200 km south, as that is the net change in his position from start to end.
Step-by-step explanation:
Alan's journey consists of three legs: he flies 400 km south to New York, then 1000 km south to Miami, and finally 1200 km north to Washington DC. To calculate the total distance covered, we add up the lengths of all legs of the journey: 400 km + 1000 km + 1200 km, which equals 2600 km. Displacement, on the other hand, is the vector quantity that denotes the change in position from the starting point to the end point, irrespective of the path taken. Alan's displacement can be found by summing up the directional components: He flies a total of 1400 km south (400 km + 1000 km) and then 1200 km north, resulting in a net displacement of 200 km south. Therefore, Alan's displacement is 200 km south.