What action should a GIS analyst take to display transit lines that are missing a projection file?

Selecting to define the existing projection using the Define Projection tool is the correct approach when dealing with transit lines that are missing a projection file. This tool allows the GIS analyst to assign a coordinate system to a dataset that does not currently have one. It does not alter the geometric data or its spatial reference but simply tells ArcGIS what coordinate system the data is supposed to be in.

This action is essential because having a defined projection ensures that the data can be properly displayed and analyzed in relation to other geographic data layers that may have different projections.

In contrast, copying a projection file from another feature class may not always be appropriate, as it assumes that the original feature class's projection is correct and applicable to the situation at hand. Using the Project geoprocessing tool would be relevant only if there is a need to convert data to a different projection rather than just defining one. Recreating the transit lines would be unnecessary and inefficient if the intent is simply to address the missing projection. Thus, defining the existing projection is the most efficient and appropriate action to take in this scenario.