01
Record the route before adding components
The first displacement is (3, 0) and the second is (0, 4). Adding corresponding components gives (3, 4), the displacement from O to B. Draw each move from the end of the previous one so that the route is continuous. A small worksheet can use columns for start point, move and end point. This prevents the two arrows from accidentally being interpreted as independent journeys from the origin. The final position follows from the ordered moves, while the combined displacement compares only the initial and final positions.
02
Calculate two different lengths
The travelled route has length 3 + 4 = 7 units. The straight displacement has magnitude square root of (3 squared + 4 squared), which is 5 units. The difference is not an error: the route follows two perpendicular legs, while the displacement joins their endpoints directly. Keep both labels beside their values. Calling either result simply distance without describing the measured path would make the worksheet ambiguous. The calculation assumes the flat Euclidean geometry shown in the drawing, not a curved surface or a road network.
03
Reverse the order as a useful check
Now travel four units north first, then three units east. The intermediate point becomes (0, 4), but the endpoint is still (3, 4). The total route length remains seven units and the direct displacement remains five. The paths themselves are different, so this check does not claim that order never matters in a journey. Obstacles, timing and other rules could make the routes behave differently. Record the changed intermediate point alongside the unchanged endpoint to show exactly which properties this simple addition preserves.