Which action would be protected by the ninth amendment?

Assuming the list of options you have is the same as I've seen elsewhere for this question, then the best answer is:  explaining medical problems to a personal physician.

In having such a conversation with a personal physician, an individual has an expectation of privacy and confidentiality.  A specific "right to privacy" is not detailed witihin the United States Constitution, but the 9th Amendment states, "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people."  The 9th Amendment has been seen as a place where rights to privacy are protected.  Famously, the case of "Roe v. Wade," which dealt with a woman seeking medical assistance in terminating a pregnancy, revolved around these issues.   "Jane Roe" was a pseudonym used for the court case.  Attorneys for "Jane Roe" challenged the state law that prohibited abortion except "”for the purpose of saving the life of the mother," with Dallas County District Attorney named as the defendant to represent the state of Texas.  The case ultimately went to the US Supreme Court and rights to privacy and the 9th Amendment became key issues in the decision.

answer: in 1900, there were no "workplace safety laws"!

explanation: at the beginning of this century, workers in the united states faced remarkably high health and safety risks on the job.

a century ago in 1900 about three hundred out of every one hundred thousand miners were killed on the job each year.

[industria] developments occurred within a legal and regulatory climate that diminished employer’s interest in safety. as a result, americans developed production methods that were both highly productive and often very dangerous.