How do I place a coordinate midway between two other coordinates using tikz

Question

I'm struggling to draw a diagram in tikz. I'm trying to do a simple illustration of a parallelogram inside an arbitrary quadrilateral.

I have the following code to place S halfway between O, and P.

Is there a way to do this? Ideally I would get a named coordinate that I can use for further drawing in the end

\documentclass{report}

\usepackage{tikz}
\usetikzlibrary{intersections, calc,through,backgrounds}

\begin{document}


\begin{tikzpicture}
%declare points OPQR at random locations
\coordinate[label=right:\textcolor{blue}{$O$}] (O) at ($(0,0) + 3*(rand, rand)$);
\coordinate[label=left:\textcolor{blue}{$P$}] (P) at ($(0,0) + -2*(rand, rand)$);

% I thought something like this would work, but it doesnt
%\coordinate[label=left:\textcolor{orange}{$S$}] (S) at ($0.5* ((O) - (P))$);

\draw[->, name path=A]  (O) -- (P);

\end{tikzpicture}

\end{document}

I also tried:

(O) -- coordinate[midway](S) (P);

but when I tried to draw a line from S to another point I got an error that pgf didn't know any shapes by the name S.

Answer 1

\coordinate (S) at ($(O)!0.5!(P)$); should solve your problem.

Answer 2

It is not clear, what is the problem. With knowing of the coordinate S you draw a rectangle. It can be simply defined as follows:

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{backgrounds,
                calc,
                intersections, 
                through}

\begin{document}
    \begin{tikzpicture}
% declare points OPQR at random locations
\coordinate[label=right:\textcolor{blue}{$O$}] (O) at ($(0,0) + 3*(rand, rand)$);
\coordinate[label=left: \textcolor{blue}{$P$}] (P) at ($(0,0) + -2*(rand, rand)$);

\draw[->, name path=A]  (O) -- coordinate[label=left:\textcolor{orange}{$S$}] (S) (P);

    \end{tikzpicture}
\end{document}