[tex](1,0)[/tex]
1) We can find algebraically the vertex of that Absolute Value inequality, by doing this procedure:
[tex]\begin{gathered} y\ge|x-1| \\ |x-1|=0 \end{gathered}[/tex]
2) Since the vertex is where the absolute value is equal to zero, let's solve as an equation, and then treat it back as an inequality to write the answer:
[tex]\begin{gathered} |x-1|=0 \\ x=1 \\ --- \end{gathered}[/tex]
Now let's plug the quantity of "x" we just found to find the y-coordinate:
[tex]\begin{gathered} y=|x-1| \\ y=|1-1| \\ y=|0| \\ y=0 \end{gathered}[/tex]
So the answer is:
[tex](1,0)[/tex]
