Shade and insert labels in a triangular region with TikZ

Here is my solution:

\documentclass[11pt]{article}
\usepackage{tikz}
\usetikzlibrary{shadings}

\begin{document}

\begin{tikzpicture} 
\draw[top color=white,bottom color=red] (0,0) -- (1,2) -- (0,3) -- cycle; 

\foreach \coordinate/\label/\pos in {{(0,0)/label1/above left},{(1,2)/label2/right},{(0,3)/label3/above right}}
\node[\pos] at \coordinate {\label};

\draw[->] (-5.0,0) -- (5.0,0) node[right] {$x$} coordinate(x axis); 
\draw[->] (0,-5.0) -- (0,5.0) node[above] {$y$} coordinate(y axis); 
\end{tikzpicture} 

\end{document}

It gives:

The key points are basically two:

1. the foreach that allows to specify in one shot the coordinate (i.e. (0,0)) in which the label will be placed in a given position (i.e. above left);

2. the use of the shadings library that allows to shade the region; in the example the shading is vertical, but it is possible to insert different type of shadings (see 47 Shadings Library from the pgfmanual version April 25, 2012 / 46 Shadings Library from the pgfmanual version October 25, 2010).

A solution with tikz and tkz-euclide

\documentclass[11pt]{scrartcl}
\usepackage{tkz-euclide}
\usetkzobj{polygons} 

\begin{document}
\begin{tikzpicture}
   \tkzInit[xmax=5,ymax=5]     
   \tkzAxeXY
   \tkzDefPoint(0,0){A}   
   \tkzDefPoint(1,2){B}
   \tkzDefPoint(0,3){C}   
   \tkzDrawPolygon[top color=white,bottom color=red](A,B,C)
   \tkzLabelPoints[above right](A,B,C)
\end{tikzpicture}   
\end{document} 

Here is an example using the patch plot type of pgfplots:

\documentclass{standalone}

\usepackage{pgfplots}


\begin{document}

\begin{tikzpicture}
    \begin{axis}
    \addplot[patch,shader=interp]
    table[point meta=\thisrow{c}] {
        x y c
        % first patch:
        0 0 0.2
        1 1 0
        2 0 1

        % second patch:
        1 1 0
        2 0 -1
        3 1 0

        % third patch:
        2 0 0.5
        3 1 1
        4 0 0.5
    };
    \end{axis}
\end{tikzpicture}

\end{document}

and with labels and continuos shading:

\documentclass{standalone}

\usepackage{pgfplots}


\begin{document}

\begin{tikzpicture}
    \begin{axis}
    \addplot[patch,shader=interp]
    table[point meta=\thisrow{c}] {
        x y c
        % first patch:
        0 0 0.2
        1 1 0
        2 0 1

        % second patch:
        1 1 0
        2 0 1
        3 1 0

        % third patch:
        2 0 1
        3 1 0
        4 0 0.5
    };
    \addplot[only marks,nodes near coords] % this produces labels
    table[point meta=explicit symbolic,meta=labels] {
        x y labels
        0 0 $a$
        1 1 $b$
        2 0 $c$
        3 1 $d$
        4 0 $e$
    };
    \end{axis}
\end{tikzpicture}


\end{document}

It uses a default axis configuration and reads points from an input table. The table has three columns: one for x, one for y, and one for the color data. The color data is mapped linearly into a colormap which can be configured, what you see is the default. The shader=interp tells pgfplots to produce a linear shading between the three corners and is color data.

The second graphics has two plots in the same axis: one which produces the geometry and one which produces nodes near coords. This is a special scatter plot which assumes that point meta contains the content of nodes which are placed at the input coordinates. In this case, I used point meta=explicit symbolic which, for table input, means that the meta column contains textual data. I chose meta=labels to idenfity the "labels" column which contains math mode text.

You may also be interested in

• axis lines=left which does not produce a box but axis lines on their lower ("left") limits,

• three dimensional plots with \addplot3 (and one more table column)

• other input formats (coordinates as in your example is also supported, even with color data)

• details for the encountered options + more examples in the pdf manual on http://pgfplots.sourceforge.net/