A courier robot starts from the origin O of a square grid in which each square represents 10m. It follows the sequence of moves listed below, always along grid lines:
Step 1: 3 squares east
Step 2: 4 squares north
Step 3: 5 squares west
Step 4: 2 squares south
Step 5: 1 square east
(i) Using x- and y-axes through O, write the coordinates of the robot after each step.
(ii) Compute the total path length (distance) travelled by the robot.
(iii) Determine the robot’s net displacement from O at the end of Step 5, giving both the ordered pair (Δx,Δy) and its magnitude to the nearest metre.
(iv) Show, with calculations, which is numerically greater: the total distance or the magnitude of the displacement, and state a brief reason.