Mathematics
Mathematics
Problem
A delivery robot starts from the warehouse located at the origin on a coordinate grid where unit represents block in the city. The robot follows these instructions in order: 1. Move blocks east. 2. Move blocks north. 3. Move blocks west. 4. Move blocks south. 5. From its present position, move to a point that is blocks left of the -axis but remains at the same height (ordinate) as the current position. Answer the following: (a) After step 4, find the coordinates of the robot. (b) After step 5, find the new coordinates of the robot and state the quadrant or axis on which it now lies. (c) If the robot must return to the warehouse using the shortest possible path consisting only of movements parallel to the axes, determine a sequence of moves (east/west/north/south) and the total distance it must travel.Intuitive explanation
This problem is about tracking position changes on a coordinate grid using vectors and understanding how each instruction shifts the robot's location. The key insight is that east/west movements change the -coordinate while north/south movements change the -coordinate—treat them independently, then combine to find the final position. Once you know where the robot ends up, returning home is just calculating the Manhattan distance back to the origin.
Intuitive explanation
This problem is about tracking position changes on a coordinate grid using vectors and understanding how each instruction shifts the robot's location. The key insight is that east/west movements change the -coordinate while north/south movements change the -coordinate—treat them independently, then combine to find the final position. Once you know where the robot ends up, returning home is just calculating the Manhattan distance back to the origin.