What must the government prove to take land by eminent domain?

The correct choice is anchored in the requirement that the government must provide "just compensation" to the landowner when exercising its power of eminent domain. This principle is derived from the Fifth Amendment of the U.S. Constitution, which states that private property shall not be taken for public use without just compensation. This provision ensures that property owners are fairly compensated for their loss when the government decides to take land for public purposes, such as building roads, schools, or other infrastructure projects.

While the other options present various scenarios regarding land use and ownership, they do not align with the primary legal requirement of just compensation. The emphasis on compensation reflects the balance between the government's need to acquire land for public benefit and the rights of individual property owners. Thus, it is vital for the government to adhere to this requirement to uphold the legal and ethical standards of property rights.