# Drawing vertical lines on a coordinate plane using Tikz

I am trying to plot the vertical lines x=0 and x=4 using the Tikz environment. What I have thus far is;

\begin{tikzpicture}[yscale=1]
% 4x4 grid
\draw (0, 0) grid (5, 5);
% origin point
\draw [color=blue, fill=black] (0, 0) circle (0.1);
\draw [color=blue, fill=blue] (1, 1) circle (0.1);
\draw [color=blue, fill=blue] (2, 1) circle (0.1);
\draw [color=blue, fill=blue] (3, 1) circle (0.1);
\draw [color=blue, fill=blue] (1, 2) circle (0.1);
\draw [color=blue, fill=blue] (2, 2) circle (0.1);
\draw [color=blue, fill=blue] (3, 2) circle (0.1);
\draw [color=blue, fill=blue] (1, 2) circle (0.1);
\draw [color=blue, fill=blue] (1, 3) circle (0.1);
\draw [color=blue, fill=blue] (2, 3) circle (0.1);
\draw [color=blue, fill=blue] (3, 3) circle (0.1);
\node at (4,-.5) {$\frac{1}{2}$};
\node at (-.5,4) {$\frac{1}{2}$};
% x-axis
\draw [thick,->] (0, 0) -- (5.5, 0);
% y-axis
\draw [thick,->] (0, 0) -- (0, 5.5);
% origin label
\node at (-0.1, -0.5) {(0, 0)};
%Labeling of points
\node at (1.25, 3.25) {$P_{1}$};
\node at (2.25, 3.25) {$P_{2}$};
\node at (3.25, 3.25) {$P_{3}$};
\node at (1.25, 2.25) {$P_{4}$};
\node at (2.25, 2.25) {$P_{5}$};
\node at (3.25, 2.25) {$P_{6}$};
\node at (1.25, 1.25) {$P_{7}$};
\node at (2.25, 1.25) {$P_{8}$};
\node at (3.25, 1.25) {$P_{9}$};
\draw [green, thick, domain=0:4] plot (\x, {0});
\draw [green, thick, domain=0:4] plot (\x, {4});
% x-axis label
\node at (6, 0) {x};
% y-axis label
\node at (0, 6) {y};
\end{tikzpicture}


The commands plot (\x {0}) and plot (\x {4}) produce the lines y=0 and y=4. I had thought that the command plot (\y {0}) and plot (\y {4} would produce the lines needed, but I only receive an error. Is there a straightforward way to plot these lines?

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Try \draw [green, thick, domain=0:4] plot ({4}, \x); –  jlv Apr 17 '14 at 2:36
Or simply \draw[green, thick] (4,0) -- (4,4);. Why do you want plot? –  Harish Kumar Apr 17 '14 at 4:18

In addition to the solutions provided in the comments, because of the repetitive pattern being found, the code can be simplified by using foreach loop and a counter called sub for subscript of labels. Many line codings are, therefore, reduced significantly by this skill.

Code

\documentclass{article}
\usepackage{tikz}
\begin{document}

New solution:

\begin{tikzpicture}[yscale=1]
\newcounter{sub}
\setcounter{sub}{1}
\draw (0, 0) grid (5, 5);  % 4x4 grid
%  for each loop
\foreach \y in {3,2,1}{
\foreach \x in {1,2,3}{
\draw [color=blue, fill=blue] (\x, \y) circle (0.1);  % for the blue cicles
\node at (\x+0.25, \y+0.25) {$P_{\thesub}$};          % for the P_sub labels
\stepcounter{sub}
}}                                                    % what follows are OP's code mainly
\node at (4,-.5) {$\frac{1}{2}$};
\node at (-.5,4) {$\frac{1}{2}$};

\node at (-0.1, -0.5) {(0, 0)};% origin label
\draw [green, thick, domain=0:4] plot ({0},\x);
\draw [green, thick, domain=0:4] plot ({4},\x);

\node at (6, 0) {x};% x-axis label
\draw [thick,->] (0, 0) -- (5.5, 0);
\node at (0, 6) {y};% y-axis label
\draw [thick,->] (0, 0) -- (0, 5.5);
\draw [color=blue, fill=black] (0, 0) circle (0.1);
\end{tikzpicture}

\end{document}

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