The Trail of Tears started in Northern Georgia and around Cherokee NC in the North Carolina mountains as well as around the Asheville area, Turned NW through Tennessee, then through southern Illinois across Missouri to then south Oklahoma.
The shortest distance between 2 points is a straight line. So, you might wonder why the routes the Indians took during Indian Removal went north, east, west, south. It certainly wasn't the shortest route.
The routes of the Trail of Tears were out of line because US supply lines were along the routes the Indians' took. The provisions in these supplies were suppose to be clothing, shoes and food. Many of these suppliers charged for the supplies that were supposed to be given. Suppliers were corrupted and often sold to others rather than the Native Americans in route to Oklahoma Indian Territory.
Often Native Americans were forced to pay to cross over settlers land. Sometimes settlers refused to let the Indians pass on their land. Sometimes settlers were kind and let the Indians stay in their out buildings and provided food and water.
Davidson, Gienapp, Heyrman, Lytle, Stoff, Nation of Nations: A narrative History of the American Republic, Volume 1, McGraw-Hill Companies. New York, NY. 2001. pgs. 341-