Putting coordinate axes on a TikZ picture

I get the following error: Package pgf Error: No shape named Q is known. Without the \begin{axis} ... \end{axis}, the code is compiled but the images depicted is a jumbled mess. I intended to get a right triangle with vertices A, P, and Q and with a right angle at Q. B is a point on the line through P and Q. How do I get a right angle drawn at Q?

\documentclass[10pt]{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools,array}

\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}


\begin{tikzpicture}
\begin{axis}
[width=6in,axis equal image,
    axis lines=middle,
    xmin=-10,xmax=10,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-4,ymax=6,
    restrict y to domain=-4:6,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\path (80:3) coordinate (a) (20:3.5) coordinate (b) (0:0) node[label=below left:$P$]{} coordinate(P)(-100:1)coordinate (e) (-160:1) coordinate (f)(80:2) node [label=above left:$A$]{} coordinate (A) (20:2.5) node [label=below:$B$]{} coordinate (B) ($(P)!(A)!(B)$) coordinate (Q) node [label=below:$Q$]{};
\draw[<->]  (a) node [above left ]{$l$} -- (e);
\draw[<->]  (b) node [below right]{$k$} -- (f);

\draw[purple!70!black,dashed] (A) -- (Q);
%\tkzMarkRightAngle(A,Q,P);

\draw[|<->|] ($(P)!3mm!90:(A)$)--node[fill=white,sloped] {$r$} ($(A)!3mm!-90:(P)$);
\draw[|<->|] ($(P)!-3mm!90:(Q)$)--node[fill=white,sloped] {$x$} ($(Q)!-3mm!-90:(P)$);
\draw[|<->|] ($(Q)!-3mm!90:(A)$)--node[fill=white,sloped] {$y$} ($(A)!-3mm!-90:(Q)$);
\path pic[draw, angle radius=5mm,"$\theta$",angle eccentricity=1.25] {angle = B--P--A};
\end{axis}
\end{tikzpicture}

    \end{document}