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Point 'fixed' in one direction
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<iframe 
    src="https://jsxgraph.org/share/iframe/point-fixed-in-one-direction" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Point 'fixed' in one direction" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID,{axis:true,boundingbox:[-1,2,2,-1], keepaspectratio: true});
    
    var A = board.create('point', [1,0]);
    var B = board.create('point', [0,1]);
    
    board.on('move', function(){
            A.moveTo([1, A.Y()]);
            B.moveTo([B.X(), 1]);
    });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

var board = JXG.JSXGraph.initBoard(BOARDID,{axis:true,boundingbox:[-1,2,2,-1], keepaspectratio: true});

var A = board.create('point', [1,0]);
var B = board.create('point', [0,1]);

board.on('move', function(){
        A.moveTo([1, A.Y()]);
        B.moveTo([B.X(), 1]);
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Point 'fixed' in one direction" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID,{axis:true,boundingbox:[-1,2,2,-1], keepaspectratio: true});
   
   var A = board.create('point', [1,0]);
   var B = board.create('point', [0,1]);
   
   board.on('move', function(){
           A.moveTo([1, A.Y()]);
           B.moveTo([B.X(), 1]);
   });
</jsxgraph>
$A$ and $B$ are free points. Whenever the board is updated, e.g. after a drag event, the x-coordinate of $A$ is set to $1$ and the y-coordinate of $B$ is set to $1$. Therefore, $A$ moves on the vertical line through $x=1$, $B$ moves on the horizontal line through $y=1$.
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID,{axis:true,boundingbox:[-1,2,2,-1], keepaspectratio: true});

var A = board.create('point', [1,0]);
var B = board.create('point', [0,1]);

board.on('move', function(){
        A.moveTo([1, A.Y()]);
        B.moveTo([B.X(), 1]);
});

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.