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I am fairly new to using ArcGIS Desktop.

I am working with two different types of data. The first is a large shapefile that contains small polygons that distinguish different types of vegetation. The second shapefile contains randomized points with coordinates attached and one or two other attributes like "Y" or "N". I'm trying to create some type of attribute table that will add the attributes of the polygon layer to the points that fall within the specific vegetation types. In practical terms, I want to know what veg type the points are sitting in.

I feel like this should be straight forward but I'm having a hard time getting joins and relates to work and I'm wondering if there is another option.

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You can use Spatial Join to join your points and polygons. The resultant points will have the attributes of the polygons

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Although this can be done using the highly flexible Spatial Join tool, a simpler tool to use, and one which has point-in-polygon overlay as one of its key use cases is the Intersect tool which:

Computes a geometric intersection of the input features. Features or portions of features which overlap in all layers and/or feature classes will be written to the output feature class.

When in_features are a point shapefile and a polygon shapefile then the out_feature_class can be a point shapefile with all attributes from both by using "ALL" for your join_attributes.

In other words, the Intersect tool can be used to transfer a copy of the polygon attributes to any points that fall within them.

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