Changing geometries but keeping attributes

I have a python script that takes a shapefile of points and moves those points to a new location. The output feature only has FID, ID, and geometry type, is there a way to preserve the attributes from the original shapefile with the new geometries.

Here is the part of the script that moves the feature, which works great:

infc = Saved_Layer
rows = arcpy.da.SearchCursor(infc, ["Easting", "Northing", "Test_Type"])
point = arcpy.Point()
pointGeometryList=[]

for row in rows:
x = row[0]
y = row[1]
TestType = row[2]
if TestType == 'MTU':
distance = .3535535
angle = 45
(disp_x, disp_y) = (distance * sin(radians(angle)),\
distance * cos(radians(angle)))
(end_x,end_y) = (x + disp_x, y + disp_y)
point = arcpy.Point(end_x, end_y)
pointGeometry = arcpy.PointGeometry(point)
pointGeometryList.append(pointGeometry)

elif TestType == 'TU':
distance = .707107
angle = 45
(disp_x, disp_y) = (distance * sin(radians(angle)),\
distance * cos(radians(angle)))
(end_x,end_y) = (x + disp_x, y + disp_y)
point = arcpy.Point(end_x, end_y)
pointGeometry = arcpy.PointGeometry(point)
pointGeometryList.append(pointGeometry)

# Create feature from geometry list
arcpy.CopyFeatures_management(pointGeometryList, "Points.shp")

fc = "Points.shp"
spatialref = arcpy.SpatialReference(prjfile)
arcpy.DefineProjection_management(fc, spatialref)



I have tried searchcursor, updateCursor, insertcursor, and spatial joins but when I use the cursor all I get is the first X and Y repeated in every row. The new geometries only need to include three fields from the original shapefile.