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ArcGIS for Desktop 10.6.1.

I have a polyline (old railroad track). I'd like to add the train stops as points along it by clicking on the places. I have georeferenced historical maps as the background and can see the train stops on it.

The help files all point to the Construct Points tool, but with that tool, I have to select distances or equal distance, or number of points. I don't see an option for clicking on the line.

If I just generate points (create a new point file and just click), then then points may not be on the line.

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If you set up Snapping so that Edge Snapping is on then you should see a SnapTip to tell you that the points you are digitizing are all on that line.

From About snapping (with my bolding):

Snapping allows you to create features that connect to each other so your edits are more accurate, with fewer errors. When snapping is turned on, your pointer will jump, or snap to, edges, vertices, and other geometric elements when your pointer is near them and within a certain tolerance. This enables you to position a feature easily in relation to the locations of other features.

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