Which US law gave settlers free land if they lived on and improved it?

The Homestead Act of 1862 offered settlers public land if they lived on it and made improvements, such as cultivating the land, for a required period. The Treaty of Guadalupe Hidalgo ended the Mexican-American War, while the Reclamation Act focused on water projects, so the correct choice is the Homestead Act.

AI-written and checked against the verified answer.