Perpendicular bissector

The construction of points on the perpendicular bissector of [AB]. It is achieved in an artisanal way, the purpose being to show how to achieve computations with pgf. A much simpler construction can certainly be done with other pgf commands but the idea here is to emphasize the analytical process.

Edit and compile if you like:

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% Perpendicular bissector
% Author:  Hugues Vermeiren
\documentclass{minimal}
\usepackage{tikz,xifthen}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
\begin{document}
        
\newcounter{index}
\setcounter{index}{0}
\begin{tikzpicture}[
        scale=1.0,
        MyPoints/.style={draw=blue,fill=white,thick},
        Segments/.style={draw=blue!50!red!70,thick},
        MyCircles/.style={green!50!blue!50,thin}
        ]
    % Warning : all this is an artisanal way of computing points
    % on the perpendicular bissector of [AB]
    % It could very well be achieved with more powerfull tools...
    % (package tkz-2d, for example)
    \clip (-2.5,-2.5) rectangle (7,7.5);
    \draw[color=gray,step=1.0,dotted] (-2.1,-2.1) grid (6.1,7.1);
    \draw[->] (-2,0)--(6.5,0) node[right]{$x$};
    \draw[->] (0,-2)--(0,7) node[above]{$y$};
    % Feel free to change here coordinates of points A and B
    \pgfmathparse{-sqrt(2)}     \let\Xa\pgfmathresult
    \pgfmathparse{2}        \let\Ya\pgfmathresult
    \coordinate (A) at (\Xa,\Ya);
    \pgfmathparse{5}        \let\Xb\pgfmathresult
    \pgfmathparse{13/3}     \let\Yb\pgfmathresult
    \coordinate (B) at (\Xb,\Yb);
    
    % Let I be the midpoint of [AB]
    \pgfmathparse{(\Xb+\Xa)/2} \let\XI\pgfmathresult
    \pgfmathparse{(\Yb+\Ya)/2} \let\YI\pgfmathresult
 
 
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