Your statement would imply that a point has a direction, which it does not. Also, a line does not have a length; both you and Posner meant line segment. So a correct statement would be:
A zero-length line segment is a point.
Edit: not even this is true if your definition of a line segment explicitly states that the endpoints must be distinct, as does PlanetMath's definition, as Aethaeryn points out below.
A zero-length line segment is a point.
Edit: not even this is true if your definition of a line segment explicitly states that the endpoints must be distinct, as does PlanetMath's definition, as Aethaeryn points out below.