Sandstone is a sedimentary rock that is primarily composed of sand-sized minerals or rock grains. When sandstone undergoes the process of metamorphism, it transforms into a new rock called quartzite. Option 1, shale, is incorrect because shale is a different type of sedimentary rock that is formed from compacted clay and silt particles. Option 2, slate, is also incorrect because slate is a fine-grained metamorphic rock that is formed from shale or mudstone. Lastly, option 4, marble, is incorrect because marble is a metamorphic rock that is formed from limestone or dolostone, not sandstone. Therefore, the correct answer is option 3, quartzite, as it accurately represents the metamorphic transformation of sandstone.