Final answer:
Chloroplasts are the organelles derived from ancestral free-living bacteria through endosymbiotic events and have characteristics such as their own DNA and a double membrane, supporting their bacterial origins.
Step-by-step explanation:
The organelle derived from ancestral free-living bacteria is the chloroplast. Chloroplasts, along with mitochondria, are well-supported by evidence to have originated from endosymbiotic events with bacteria. This theory, known as the Endosymbiotic Theory, was first proposed by Lynn Margulis in 1967 and suggests that chloroplasts evolved from photosynthetic bacteria, likely cyanobacteria, that were engulfed by primitive eukaryotic cells.
The engulfed bacteria formed a symbiotic relationship with their host cell, eventually becoming the organelles known as chloroplasts. These chloroplasts have characteristics such as their own DNA and a double membrane structure that are indicative of their bacterial origins. The inner membrane is believed to have come from the cyanobacterial ancestor's own plasma membrane, while the outer membrane is from the host cell's vacuole that originally engulfed the bacteria.
Chloroplasts are found in plant cells and some algae, and they are responsible for photosynthesis. They have a double membrane and their own DNA, which is similar to the DNA found in cyanobacteria. This suggests that chloroplasts originated from an endosymbiotic event in which a primitive eukaryotic cell engulfed a cyanobacterium.