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I am looking to calculate the distance from a main point to multiple points WITHIN shapefile. In other words: I have a main point at the mouth of a creek. I have about 1,200 points at various distances upstream from the mouth. I would like to calculate the distance from the mouth to each individual point. (aka, mouth to point 1, mouth to point 2, mouth to point 3, etc.) So, in the end, I would end up with 1,200 measurements, all starting at the mouth of the creek. I can only find tools that measure Euclidean distance or measure distance BETWEEN two consecutive points along a line, which will not work. I am looking for something that measures distance ALONG the route of the creek from one main point to multiple other points. Any tips?
Screenshot image: want to find individual measurements from mouth point (red) to each blue point.
I'm using ArcGIS 10.3.1. I have no experience with Python.