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
a. (i) Using x- and y-axes through O, write the coordinates of the robot after each step.
b. (ii) Compute the total path length (distance) travelled by the robot.
c. (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.
d. (iv) Show, with calculations, which is numerically greater: the total distance or the magnitude of the displacement, and state a brief reason.