I'm trying to add an attribute value to a new PointGeometry before I write it into the new file. How do I do that with arcpy?

Let's say in this example I want to write the ID of the line feature into the new point feature:

points = []
for row in arcpy.da.SearchCursor('lineFeature', ("ID", "SHAPE@")): 
    length = int(row[1].length)
    for i in xrange(0, length, 10): 
        point = row[1].positionAlongLine(i)
        # should write the ID here
        # something like 
        # point.setValue('sourceID', row[0])
        points.append(point)    
arcpy.CopyFeatures_management(points, 'pointsFeature') 

The command point.setValue('sourceID', row[0]) point. doesn't work, it returns:

Runtime error
Traceback (most recent call last):
File "<string>", line 8, in <module>
AttributeError: 'PointGeometry' object has no attribute 'setValue'