The correct answer to this open question is the following.
The most settlement by Americans from 1850-1890 can be found in the states of Texas and California.
After the victory of the United States over Mexico in the Mexican American War of 1848, the US gained a huge portion of land. One important industry that triggered the settling of the new territories was the railroad industry, specifically the Transcontinental Railroad that started the construction of new rails in 1864. The Transcontinental Railroad connected the East with the West of the US. The construction ended on May 10, 1860, in Promontory, Utah. Trade and transportation improved with the new railroad.
France transferred the Louisiana Territory to "Spain" after the French and Indian War, although it should be noted that not all of the territory went to Spain, with some of it initially going to England.
It was originally intended to shorten the sailing time between the Atlantic and Pacific Oceans. Were it not there, a ship would have to travel to the lowest tip of South America and back up again. It would extend any trip by not a trivial amount of time.
