Final answer:
Points are zero-dimensional, lines are one-dimensional, and planes are two-dimensional objects in an automatic system as related to geometry and coordinate systems.
Step-by-step explanation:
In an automatic system, the categories points, lines, and planes reflect objects of varying dimensions. A point is an example of a zero-dimensional object because it specifies a single location in space but has no length, width, or depth. A line is one-dimensional as it has length but no width or depth, providing a straight path between two points. A plane is a two-dimensional object with length and width but no depth, like a flat surface that extends infinitely in two directions.
In summary, points belong to category (a) Zero-dimensional objects, lines correspond to category (b) One-dimensional objects, and planes fall into category (c) Two-dimensional objects. This classification is essential in geometry and is also pertinent when working with vectors and coordinate systems in mathematics and physics.