If and when one starts learning about this, you will learn that the 9th week is when the embryo becomes a fetus. There's a clear distinction in that.
But that pregnancy doesn't involve another person at that point. To be a 'person' there must be some agency in action. Not just reaction to stimulation, pain, whatever- there must be independent actions. At the 16th week it happens:
"His or her eyes can slowly move.
"Your baby's limb movements are becoming coordinated..."
Fourteen weeks into your pregnancy, or 12 weeks after conception, your baby's neck has become more defined. Red blood cells are forming in your baby's spleen.
Your baby's sex will become apparent this week or in the coming weeks.
By now your baby might be almost 3 1/2 inches (87 millimeters) long from crown to rump and weigh about 1 1/2 ounces (45 grams).
Week 15: Baby's scalp pattern develops
Fifteen weeks into your pregnancy, or 13 weeks after conception, your baby is growing rapidly. Bone development continues and will soon become visible on ultrasound images. Your baby's scalp hair pattern also is forming.
Week 16: Baby's eyes move
Fetal development 14 weeks after conception
Sixteen weeks into your pregnancy, or 14 weeks after conception, your baby's head is erect. His or her eyes can slowly move. The ears are close to reaching their final position. Your baby's skin is getting thicker.
Your baby's limb movements are becoming coordinated and can be detected during ultrasound exams. However, these movements are still too slight to be felt by you.
By now your baby might be more than 4 1/2 inches (120 millimeters) long from crown to rump and weigh close to 4 ounces (110 grams).