A delivery robot starts from the warehouse located at the origin on a coordinate grid…

MATHEMATICS · Subjective · AoPS · Mathematics · Lines Graphing · Lines Graphing

Problem

A delivery robot starts from the warehouse located at the origin W(0,0)W(0,0) on a coordinate grid where 11 unit represents 11 block in the city. The robot follows these instructions in order: 1. Move 66 blocks east. 2. Move 55 blocks north. 3. Move 33 blocks west. 4. Move 22 blocks south. 5. From its present position, move to a point that is 44 blocks left of the yy-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.

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