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I would like to create random points across my study area (which is a DEM raster) using the Feature Class> Create Random Points. However, I need to select/copy/move/delete these points and re-arrange them in a line, with each point 1km away from each other. I was wondering whether there is a specific tool that I can use in ArcMap 10.1 to achieve this i.e. a tool that can tell me how far each point is from another point or is there way to measure the distance between two points to ensure I am placing these points exactly 1km away?

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PointMaker will allow you to create points using a variety of point patterns including random, random in circle or ellipse, grid and linear with several variants. It sounds like you want to create them in a grid or linear pattern with or without rotation.

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