Which dimension is linear and can measure the efficient distance on a projected surface?

The scale factor is the correct answer because it directly relates to the measurement of distances on a projected surface. In surveying and cartography, the scale factor describes how distances on a map or a projection relate to the actual distances on the Earth's surface. It accounts for the distortion that occurs when projecting the three-dimensional Earth onto a two-dimensional surface.

In the context of a projected surface, the scale factor allows surveyors to convert linear measurements made on a map into actual distances, ensuring accuracy in distance calculations. The scale factor can vary across different regions of the map, reflecting how geographic features and distances may be distorted due to the projection method used.

Latitude and longitude, while also important geographic coordinates, do not measure linear distances in a straightforward manner on projected surfaces. Elevation pertains to vertical measurements and does not provide information about horizontal distances. Therefore, when measuring efficient distances on a projected surface, understanding the scale factor is crucial for accurate interpretations and calculations in surveying tasks.