How does discovering that Blue eyes/Achilles is her brother influence Placidia’s thinking and change how she feels about her father?

Placidia seems to have a close relationship with her father, Quincey Valois Fincher, but her perception of him changes when she discovers that he fathered a child with a slave girl while Placidia's mother was alive and allowed that child to be sold away.

In light of recent genetic evidence showing that many of our country's founding fathers, including Thomas Jefferson and George Washington, maintained "shadow" families of mixed-race descendants on their plantations, discuss the significance of this part of America's history.

How do you think high-society Americans in the eighteenth and nineteenth centuries rationalized the sexual exploitation of enslaved African American women?

High society white men used slaves for sexual satisfaction in the same way they used them for anything else. They were slaves. They were considered property. It wasn't right based on today's standards. And there must have been somewhat of a secretive approach to such acts even at the time, as it wasn't something they advertised. But I would bet that is for the protection of high society's white men from it's white women.
Placidia certainly learns a lot during her time as a wife, and unfortunately she learns of the less than savory behavior of some men, even that of her father. In all that she is experiencing during this time, alongside her own rape and treatment as an object rather than a person, learning of her father's behavior was probably just another twig on a pile of sticks.

She loved and respected her father. Even though she knew what other men did to their slaves I think she most likely thought her father was above that. To find out he was not and that he had a child and that her mother made him sell the mistress and her son had to be disheartening.

It is clear that it totally changed her feelings towards her father. It was something she would never have considered him doing prior to then.

She comes to realize that Blue-Eyes was her half-brother who, with his slave mother, was forced to leave the farm when he was a young boy.

The discovery of her father's transgressions only serves to cause her more distrust of men in positions of power and serves to give her more empathy with the slaves' powerlessness.

It's amazing how timely this issue is right now in America. Placidia felt close to and admired her father, and idealized her understanding of her parents' relationship. She was in shock to discover what had really happened -- and later to make the connection between Nolan's forcing himself on a slave at his sister's wedding, her own father's abuse of his white male privilege, and her own rape. Up till then, she had thought of rape as something women had to fear only from slaves or from ignorant, lower class white men, like those pretending to be soldiers who invaded her farm. She was able to disapprove but largely ignore what "genteel" white men were doing to female slaves. To realize that this was an evil built right into the system that her own family lived by, something her own father had done, was first a shock to her understanding, and then a trauma, when her own rape made her realize what it had been like for the slave woman who was Achilles's mother. We can infer from her naming and her raising of her son Achilles, his memory of her wanting to create a better world, that she fully accepted the slave Achilles as a brother. In gratitude for his effort to protect her from Nolan, and all that followed, she was prepared to sacrifice the man she loved, her reputation and her life, rather than betray him back into slavery. I think there was a part of her that never forgave her father, and that is what led her to preserve her diary, the sole record of her father's abuse as well as her enslaved brother's heroism. On some level, she wanted to set straight the historical record, to speak truth to power.

Most young women idolize their fathers to some extent. When Placidia discovers the genetic relationship between her and Blue Eyes, her innocent love for her father is shattered. She had been shielded from the sexual cravings of men growing up in the 1800"s, but within a short span of time she becomes rudely mature and initiated into the exploitation many men exert over women.

There is also a Biblical parallel to this part of the story. The relationship between Abraham, Sarah and Hagar mirrors the story of Placidia's father, wife and slave.

Slaves and wives and children at that time were considered property belonging to the man. He could do with them as he chose. Placidia was the typical little girl that idolized her father. Many fathers at that time did try to shield their daughters from their exploitations.

With DNA tests now readily available I suspect more and more stories of the “shadow families” will come to light.

Placidia had a wonderful relationship with her father. She was a bit of a wild child in regard to loving horses and letting go when she rode— not the "lady like" thing to do. This created a special bond with her father. She also felt her father was a very fair man in his dealing with the slaves. Finding out that Achilles was her half-brother, revealed a side of her father she didn't know. It was a disappointment for her.

I think Dia was very upset when she realized Achilles was her half-brother and lost some respect for her father.