Question

To show that, line.length from shapely geometry is just a Euclidean distance, one can compute like this:

import math
x1, y1 = (12875996.563923, -3940011.116702)
x2, y2 = (12872802.929335, -3937989.118438)
math.hypot(x2-x1,  y2-y1)  # 3779.91783790157

To get correct distance with pyproj module, follow these steps:

import pyproj  #v2.4.1
x1, y1 = (12875996.563923, -3940011.116702)
x2, y2 = (12872802.929335, -3937989.118438)
lon1, lat1 = pyproj.Proj("epsg:3857")(x1, y1, inverse=True)
lon2, lat2 = pyproj.Proj("epsg:3857")(x2, y2, inverse=True)
_,_,dist_km = pyproj.Geod(ellps='WGS84').inv(lon1, lat1, lon2, lat2)
dist_km   # 3157.214113925091

Accepted Answer

To show that, line.length from shapely geometry is just a Euclidean distance, one can compute like this:

import math
x1, y1 = (12875996.563923, -3940011.116702)
x2, y2 = (12872802.929335, -3937989.118438)
math.hypot(x2-x1,  y2-y1)  # 3779.91783790157

To get correct distance with pyproj module, follow these steps:

import pyproj  #v2.4.1
x1, y1 = (12875996.563923, -3940011.116702)
x2, y2 = (12872802.929335, -3937989.118438)
lon1, lat1 = pyproj.Proj("epsg:3857")(x1, y1, inverse=True)
lon2, lat2 = pyproj.Proj("epsg:3857")(x2, y2, inverse=True)
_,_,dist_km = pyproj.Geod(ellps='WGS84').inv(lon1, lat1, lon2, lat2)
dist_km   # 3157.214113925091