Now you ask where in the constitution this right originates.
In the original document there was no Bill of Rights simply because the fathers did not see a need explaining that the Const. itself provided those rights enumerated in the BOR.
However some of the original founders felt there might be a mis-understanding down the road so they all agreed to draft and ratify a Bill of Rights and that is what we see now in the smithsonian.
Now while the main body of the Constitution spells out what the Government may do and what it must do; the Bill of Rights spells out what the Government MAY NOT DO.
It can't search or seize your property without due process
It cannot hold you in prison without trial
It can't enact laws abridging the freedom of speech/religion/or the right to bear arms.
And various other prohibitions on Government activity are spelled out.
The Ninth and Tenth amendmendts were enacted to make sure there was absolutely no mis-understanding concerning the LIMITED power of the government granted by the Constitution.
Amendmendt IX The enumeration in the constitution of certain rights shall not be construed to deny or disparage others retained by the people.

Amendment X The powers not delegated to the United States by the Constitution nor prohibited by it to the states are reserved to the states respectively or TO THE PEOPLE.

Now where is the right to privacy? It is clearly in those two amendmendts and the Bill of Rights.
The Government has no power to tell people what to do except in areas specifically authorised in the Constitution.

You can't find the right to privacy spelled out in the Constitution? You can't find a right to be married spelled out either; or any other personal right. But that doesn't mean it isn't there.