Final answer:
All the given coordinates are the same distance from the origin (0,0), so any of them will make GH the longest possible line segment under the given conditions.
Step-by-step explanation:
The question asks us about the longest possible line segment GH with one endpoint at the origin (0,0) on a coordinate system. To find the longest segment, we need to understand the geometry of the coordinate system. A line segment would be longest when the other endpoint lies farthest from the origin. Since the coordinates (1,0), (0,1), (-1,0), and (0,-1) are all one unit away from the origin, they are all equal in length. However, in terms of lateral movement, points (1,0) and (-1,0) represent horizontally to the right and left side of the coordinate system respectively, while points (0,1) and (0,-1) represent vertically upward and vertically downward in the coordinate system. For the segment to be the longest on a conventional two-dimensional plane, however, the direction does not matter as the length is the same in all four directions due to the symmetry of the coordinate system. Since the question asks for the longest possible segment, but all options are of the same length, any of the given coordinates may represent the other endpoint of GH, making GH the longest possible line segment under these conditions.