[Tex/LaTex] Putting coordinate axes on a TikZ picture

pgfplotstikz-pgf

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}

Best Answer

This is one way of doing it. Firstly, the proposal converts points into axis cs coordinate so that they are comparable with the pgfplot axis.

The right angles on the triangle are found via intersections of grid lines notion, that is, finding intersection points of parallel lines that are parallel to lines A-Q and P-Q.

enter image description here

Code

\documentclass[border=10pt]{standalone}%[10pt]{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools,array}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[width=6in,axis equal image,
    axis lines=middle,
    xmin=-2,xmax=4,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-2,ymax=3,
    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}
]
% Convert all points into axis cs system
\node[] at (axis cs: {3*cos(80)},{3*sin(80)})       (a){};
\node[] at (axis cs: {3.5*cos(20)},{3.5*sin(20)}) (b){};
\node[label=below left:$P$] at (axis cs: 0,0)     (P){};
\node[] at (axis cs: {1*cos(-100)},{1*sin(-100)}) (e){}; 
\node[] at (axis cs: {1*cos(-160)},{1*sin(-160)})  (f){};
\node[label=above left:$A$] at (axis cs: {2*cos(80)},{2*sin(80)})(A){}; 
\node[label=below:$B$] at (axis cs: {2.5*cos(20)},{2.5*sin(20)}) (B){} ;
\node[label=below right:$Q$,coordinate] at ($(P)!(A)!(B)$) (Q){};
\node [] at (axis cs:0.5,3){$l$};
\node [] at (axis cs:3,0.9){$k$};
\draw[<->]  (a) -- (e);
\draw[<->,name path=linea]  (b) -- (f);                   % added path name
\draw[purple!70!black,dashed,name path=lineb] (A) -- (Q); % added path name
%
\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};

% draw parallel lines
\path[name path=line1,red]  ([yshift=1cm]$(P)!0!(Q)$) -- ([yshift=1cm]$(P)!1!(Q)$);
\path[name path=line2,red]  ([yshift=-2cm]$(A)!0!(Q)$) -- ([yshift=-2cm]$(A)!1!(Q)$);

% find intersections
\path [name intersections={of=line1 and line2,by={E}}];  % corner tip
\path [name intersections={of=line2 and linea,by={E2}}];
\path [name intersections={of=line1 and lineb,by={E1}}];

% draw the right angle
\draw[red] (E1)--(E)--(E2);
\end{axis}

\end{tikzpicture}
\end{document}
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