¿Cómo traducir y rotar en TikZ en un bucle foreach para animar?

Question

Me gustaría animar el segmento horizontal al vertical, girándolo alrededor de su punto medio y trasladándolo. Mira el gif a continuación.

No tengo idea de por qué la traducción no funciona como esperaba. El segmento morado debería moverse a la posición azul final.

MWE

\documentclass[tikz,margin=2mm]{standalone}
\usetikzlibrary{calc}

\begin{document}
\foreach \a in {0,1,...,10}{%
\begin{tikzpicture}
\useasboundingbox (-.2,-1.2) rectangle (4.2,2.2);
\draw[help lines] (0,0) grid (4,2);

\draw[red] (1,0) -- +(1,0);
\draw[blue] (2,1) -- +(0,1);

\draw[thick] (1,0)++(\a/10,\a/10) -- +(1,0); % translation

\draw[thick] let \p1=(1,0), \p2=(2,0) in [rotate around={-9*\a:(1.5,0)}] (\p1) -- (\p2) ; % rotation around mid point

\draw[thick,red!50!blue,shift={+(\a/10,\a/10)}] let \p1=(1,0), \p2=(2,0) in [rotate around={-9*\a:(1.5,0)}] (\p1) -- (\p2) ; % rotation + translation WRONG!!

\end{tikzpicture}
}
\end{document}

Answer 1

No estoy seguro de entender tu problema. ¿Es esto lo que quieres?

\documentclass[tikz,margin=2mm]{standalone}
\usetikzlibrary{calc}

\begin{document}
\foreach \a in {0,1,...,10}{%
\begin{tikzpicture}
\useasboundingbox (-.2,-1.2) rectangle (4.2,2.2);
\draw[help lines] (0,0) grid (4,2);

\draw[red] (1,0) -- +(1,0);
\draw[blue] (2,1) -- +(0,1);

%\draw[thick] (1,0)++(\a/10,\a/10) -- +(1,0); % translation

%\draw[thick,green!20!black] let \p1=(1,0), \p2=(2,0) in [rotate around={-9*\a:(1.5,0)}] (\p1) -- (\p2) ; % rotation around mid point

\draw[thick,red!50!blue,shift={(\a/20,\a*1.5/10)}
] 
    let \p1=(1,0), 
        \p2=(2,0) in 
    [rotate around={-9*\a:(1.5,0)}] 
    (\p1) -- (\p2) ; % rotation + translation WRONG!!

\end{tikzpicture}
}
\end{document}

Answer 2

Creo que deberías agregar la línea:

\draw [green,rotate around={-9*\a:(2,0.1*\a)}] (1,0.1*\a) -- (2,0.1*\a); %Correct rotation

Entonces quedaría así:

\documentclass[tikz,margin=2mm]{standalone}
\usetikzlibrary{calc}

\begin{document}
\foreach \a in {0,1,...,10}{%
\begin{tikzpicture}
\useasboundingbox (-.2,-1.2) rectangle (4.2,2.2);
\draw[help lines] (0,0) grid (4,2);

\draw[red] (1,0) -- +(1,0);
\draw[blue] (2,1) -- +(0,1);

\draw[thick] (1,0)++(\a/10,\a/10) -- +(1,0); % translation

\draw[thick] let \p1=(1,0), \p2=(2,0) in [rotate around={-9*\a:(1.5,0)}] (\p1) -- (\p2) ; % rotation around mid point

\draw[thick,red!50!blue,shift={+(\a/10,\a/10)}] let \p1=(1,0), \p2=(2,0) in [rotate around={-9*\a:(1.5,0)}] (\p1) -- (\p2) ; % rotation + translation WRONG!!

%\draw [magenta,rotate around={-9*\a:(2,0)}] (1,0) -- (2,0); %rotation

%\draw [yellow] (1,0.1*\a) -- (2,0.1*\a);%translation vertical

\draw [green,rotate around={-9*\a:(2,0.1*\a)}] (1,0.1*\a) -- (2,0.1*\a); %Correct rotation

\end{tikzpicture}
}
\end{document}