Setting labels closer to the coordinates that they represent

Question

A pentagon is drawn from the following code. I label the vertices A, B, C, D, and P. The labels are too far from the points that they represent. I used the label option for the coordinate command to place the labels about their points. So, I thought that the labels would be placed directly over the coordinates, which wouldn't have been appropriate. (I was told that having an angle specified, such as 180, provides some "padding" about the point.) I would still have needed a command to move the label. I now know they syntax for moving the label about the point is

[label distance=<distance>]<angle>:<name for the label> .

What is the default distance between a point and its label? How much padding is added when an angle is specified. I would like to either suppress this padding or use label distance=<distance> to compensate for it.

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections}


\begin{document}


\begin{tikzpicture}

\coordinate[label={225:$A$}] (A) at (-0.5,-0.75);
\coordinate[label={135:$B$}] (B) at (-0.5,0.5);
\coordinate[label={45:$C$}] (C) at (1,0.5);
\coordinate[label={-45:$D$}] (D) at (1,-0.75);

\draw (A) -- (B) -- (C) -- (D) -- (A) -- cycle;

\path (A) -- (C);
\path (B) -- (D);

\path[name path=ray1] (C) -- ($(C)!1.5cm!90:(A)$);
\path[name path=ray2] (D) -- ($(D)!1.5cm!-90:(B)$);


\coordinate[name intersections={of=ray1 and ray2,by={P}}];
\node[label={right:$P$}] at (P) {};


\draw (C) -- (P) -- (D);

%\draw[line width=0.1pt, draw=gray!25] (current bounding box.south west) grid (current bounding box.north east);
\end{tikzpicture}

\end{document}

Answer 1

You can apply the label distance=<distance> style. In the following I applied this style to A, D and P, but not B and C so that the effect can be seen:

Code:

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections}
\begin{document}
\begin{tikzpicture}
\coordinate[label={[label distance=-3pt]225:$A$}] (A) at (-0.5,-0.75);
\coordinate[label={135:$B$}] (B) at (-0.5,0.5);
\coordinate[label={45:$C$}] (C) at (1,0.5);
\coordinate[label={[label distance=-3pt]-45:$D$}] (D) at (1,-0.75);
\draw (A) -- (B) -- (C) -- (D) -- (A) -- cycle;
\path (A) -- (C);
\path (B) -- (D);
\path[name path=ray1] (C) -- ($(C)!1.5cm!90:(A)$);
\path[name path=ray2] (D) -- ($(D)!1.5cm!-90:(B)$);
\coordinate[name intersections={of=ray1 and ray2,by={P}}];
\node[label={[label distance=-5pt]right:$P$}] at (P) {};
\draw (C) -- (P) -- (D);
%\draw[line width=0.1pt, draw=gray!25] (current bounding box.south west) grid (current bounding box.north east);
\end{tikzpicture}
\end{document}