A boy starts at point O on an open playground. He follows the route given below, always moving in straight lines along the cardinal directions.
Step 1: 100 m due north to point A.
Step 2: 80 m due east to point B.
Step 3: 60 m due south to point C.
Step 4: 30 m due west to point D.
(i) Draw a labelled sketch of the complete path O → A → B → C → D.
(ii) Calculate the total distance the boy covers.
(iii) Using a geometrical method, find the magnitude of the displacement from O to D, showing all working.
(iv) State the compass direction of this displacement with respect to point O.
(v) Compare your answers to parts (ii) and (iii), and explain briefly why they differ.