Final answer:
The lake where Mormon settlers established a community along its shores in Utah is the Great Salt Lake, which is option d). This location was chosen after their trek along the Mormon Trail and became central to the founding of their religious society, following years of persecution.
Step-by-step explanation:
The lake that the Mormon settlers made their home along the shores of in Utah is d) Great Salt Lake. This lake is historically significant because it was near this location that the Mormon Trail ended. After facing religious persecution in Missouri and Illinois and the murder of their founder Joseph Smith, members of the Church of Jesus Christ of Latter-day Saints, also known as Mormons, followed Brigham Young westward. They sought a remote area where they could practice their faith freely, and the Great Salt Lake region, which at that time was a sparsely-populated province of Mexico, provided such a refuge.
After the Mexican-American War, the Treaty of Guadalupe Hidalgo ceded the area to the United States, and it was incorporated into the United States as a territory. The Mormons then found themselves part of the U.S. again, with Brigham Young appointed as the territorial governor by President Millard Fillmore. Despite their struggles, the isolation of Utah helped to build and maintain a unique cultural and religious community for the Latter-day Saints.