Answer: √2km N45°E
Explanation:His displacement is the shortest distance from his starting point, so, the hypotenuse represent his displacement. Using the four cardinal point diagram, mark 1km due east on the diagram and the from that point, 1km due North, and then join the start and the end point together to form a right-angled triangle! Then solve using Pythagoras theorem or triangle method to find your displacement and using SOHCAHTOA, you can find the angle of displacement or the direction.
Pythagoras theorem
Hyp² = opp² + adj²
SOHCAHTOA means
Sin ∅ = Opp/hyp
Cos ∅ = adj/hyp
Tan ∅ = opp/adj
Using any of those, you will have the same answer for your direction.