To solve the problem of identifying the undefined geometric term described as an infinite set of points that has length but not width, we need to understand the definitions of the given options:
1. Distance: The length of the shortest path connecting two points. Distance itself does not describe an infinite set of points; rather, it is a measurement between two specific points.
2. Line: A straight one-dimensional figure having no thickness and extending infinitely in both directions. It fits the description of an infinite set of points that has length but not width.
3. Plane: A flat, two-dimensional surface that extends infinitely in all directions. A plane has both length and width, so it does not fit the description.
4. Sphere: A three-dimensional object where all points on the surface are equidistant from the center. A sphere has volume and does not fit the description of a one-dimensional figure.
Given these definitions, the correct option is line, as it is the one geometric term that accurately describes an infinite set of points with length but no width.
So, the answer is:
line
