The question is easy to explain with this MWE:
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [very thin, color=gray, dashed] (0, 0) grid (5, 5);
\draw [color=green!50!black, ->] (0, 0) -- (3,3) node[above right]{$\vec{A}$};
\draw (0,5) node[below right]{graph 1};
\end{tikzpicture}
\begin{tikzpicture}[x=0.5cm, y=0.5cm]
\draw [very thin, color=gray, dashed] (0, 0) grid (5, 5);
\draw [color=green!50!black, ->] (0, 0) -- (3,3) node[above right]{$\vec{A}$};
\draw (0,5) node[below right]{graph 2};
\end{tikzpicture}
\begin{tikzpicture}[scale=0.5]
\draw [very thin, color=gray, dashed] (0, 0) grid (5, 5);
\draw [color=green!50!black, ->] (0, 0) -- (3,3) node[above right]{$\vec{A}$};
\draw (0,5) node[below right]{graph 3};
\end{tikzpicture}
\end{document}
which results in:

In the output, graph2 did quite surprise me --- it seems that the grid and the -- to draw lines are using different coordinates. I was expecting that the grid would scale down as the line do... what am I missing?
(BTW --- also the fact that in neither graph the text is scaling down is quite surprising).


grid's optionstepis1cm, not thexoryunit, whose default is also1cm. – Heiko Oberdiek Mar 15 '15 at 21:53