How to cut a horizontal line by a perpendicular line?

Question

I'd like to cut the line AC at the point p by a perpendicular line.

\documentclass{article}
\usepackage{xypic}
\begin{document}
\xymatrix{
& B\ar @{-}[d] &\\
A\ar @{-}[rr]_{P} &  & C
  }
\end{document}

Answer 1

To extend the vertical line down to the line AC, use the arrow adjustment facility placing +0{} after the arrow. By default the arrow stops short of the center of the node, this adjustment makes it stop distance 0 from the center instead.

\documentclass{article}

\usepackage{xypic}

\begin{document}
Adjusted:
\xymatrix{
& B\ar @{-}[d]+0{} &\\
A\ar @{-}[rr]_{P} &  & C
  }

Unadjusted:
\xymatrix{
& B\ar @{-}[d] &\\
A\ar @{-}[rr]_{P} &  & C
  }

\end{document}

Such adjustments are described in Section 2.6 of the xypic User guide with something like this set as an exercise.