Give an example of hispanic lands being turned over the United States (New Mexico History)

After the United States invaded some territories in Mexico like Texas between 1846 to 1848, also known as the Mexican-American War, Mexico was forced to cede its territory in the north of the Rio Grande and California, known nowadays as the American Southwest to the United States of America through treaties with Manuel de la Peña and Peña, this was in order to make an exchange so the US military will back off the Mexican territories they had occupied. Nevertheless, Mexico was paid the amount of fifteen million dollars, plus the forgiveness of three million dollars debt that the United States claimed. Later on, on September 9th, 1850 Following a compromise, the US government established the New Mexico Territory including most part of Arizona, New Mexico and parts of Colorado, also establishing its capital Santa Fe in 1851. Moreover, in 1853 the United States bought La Mesilla, lands that are now part of Arizona and New Mexico, which were part of a plan for the southern route of the transcontinental railroad.

After the Texas Independence in 1836, war broke between Mexico and the U. S. Texas was still part of Mexico however they were governed independently and Mexico consider it as a rebel state. From 1846 through 1848 Mexico and the U. S. maintained a war that was won by the U. S. which resulted in Mexico being broke hence Antonio López de Santa Anna, President of Mexico at the time, turned over almost half of Mexican land to the U. S. and took a payment of 15 million USD. Those lands are now known as California, Texas, Utah, Colorado, Arizona, New Mexico and Nevada. Afterwards, in 1853, La Mesilla was turned over to the U. S. which is a portion of land south of New Mexico.