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Mutually dependent line and gliders
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/mutually-dependent-line-and-gliders" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Mutually dependent line and gliders" 
    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, {
        boundingbox: [-5, 5, 5, -5],
        keepaspectratio: true,
        axis: true
    });
    
    var line0 = board.create('line', [[-1, 0], [-1, 1]], {
        strokeOpacity: .2,
        strokeColor: '#000000',
        fixed: true,
        name: 'x=-1',
        withLabel: true,
        label: { position: '10% right', distance: 0.1 }
    });
    var line1 = board.create('line', [[1, 0], [1, 1]], {
        strokeOpacity: .2,
        strokeColor: '#000000',
        fixed: true,
        name: 'x=1',
        withLabel: true,
        label: { position: '10% right', distance: 0.1 }
    });
    
    var gl1 = board.create('glider', [0, 0, line0], { name: 'b' });
    var gl2 = board.create('glider', [1, -1, line1], { name: 'a' });
    
    var line = board.create('line', [gl1, gl2]);
    
    // offset determines the slope of line
    var offset = gl2.Y() - gl1.Y();
    
    // Drag gl1 and keep the slope of the line
    gl1.on('drag', function() {
        gl2.moveTo([gl1.X(), gl1.Y() + offset]);
    });
    
    // Drag gl2 and adapt the slope of the line
    gl2.on('drag', function() {
        offset = gl2.Y() - gl1.Y();
    });
 </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, {
    boundingbox: [-5, 5, 5, -5],
    keepaspectratio: true,
    axis: true
});

var line0 = board.create('line', [[-1, 0], [-1, 1]], {
    strokeOpacity: .2,
    strokeColor: '#000000',
    fixed: true,
    name: 'x=-1',
    withLabel: true,
    label: { position: '10% right', distance: 0.1 }
});
var line1 = board.create('line', [[1, 0], [1, 1]], {
    strokeOpacity: .2,
    strokeColor: '#000000',
    fixed: true,
    name: 'x=1',
    withLabel: true,
    label: { position: '10% right', distance: 0.1 }
});

var gl1 = board.create('glider', [0, 0, line0], { name: 'b' });
var gl2 = board.create('glider', [1, -1, line1], { name: 'a' });

var line = board.create('line', [gl1, gl2]);

// offset determines the slope of line
var offset = gl2.Y() - gl1.Y();

// Drag gl1 and keep the slope of the line
gl1.on('drag', function() {
    gl2.moveTo([gl1.X(), gl1.Y() + offset]);
});

// Drag gl2 and adapt the slope of the line
gl2.on('drag', function() {
    offset = gl2.Y() - gl1.Y();
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Mutually dependent line and gliders" 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, {
       boundingbox: [-5, 5, 5, -5],
       keepaspectratio: true,
       axis: true
   });
   
   var line0 = board.create('line', [[-1, 0], [-1, 1]], {
       strokeOpacity: .2,
       strokeColor: '#000000',
       fixed: true,
       name: 'x=-1',
       withLabel: true,
       label: { position: '10% right', distance: 0.1 }
   });
   var line1 = board.create('line', [[1, 0], [1, 1]], {
       strokeOpacity: .2,
       strokeColor: '#000000',
       fixed: true,
       name: 'x=1',
       withLabel: true,
       label: { position: '10% right', distance: 0.1 }
   });
   
   var gl1 = board.create('glider', [0, 0, line0], { name: 'b' });
   var gl2 = board.create('glider', [1, -1, line1], { name: 'a' });
   
   var line = board.create('line', [gl1, gl2]);
   
   // offset determines the slope of line
   var offset = gl2.Y() - gl1.Y();
   
   // Drag gl1 and keep the slope of the line
   gl1.on('drag', function() {
       gl2.moveTo([gl1.X(), gl1.Y() + offset]);
   });
   
   // Drag gl2 and adapt the slope of the line
   gl2.on('drag', function() {
       offset = gl2.Y() - gl1.Y();
   });
</jsxgraph>

Mutually dependent line and gliders

Geometry
Glider
In this example, $a$ and $b$ are gliders on lines. Additionally, the glider $a$ depends on glider $b$ in the following way: if $a$ is dragged, $b$ is moved accordingly too such that the slope of the line is constant. If $b$ is dragged, the slope of the line is adapted. Here, we need JSXGraph events to realize this behavior.
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    keepaspectratio: true,
    axis: true
});

var line0 = board.create('line', [[-1, 0], [-1, 1]], {
    strokeOpacity: .2,
    strokeColor: '#000000',
    fixed: true,
    name: 'x=-1',
    withLabel: true,
    label: { position: '10% right', distance: 0.1 }
});
var line1 = board.create('line', [[1, 0], [1, 1]], {
    strokeOpacity: .2,
    strokeColor: '#000000',
    fixed: true,
    name: 'x=1',
    withLabel: true,
    label: { position: '10% right', distance: 0.1 }
});

var gl1 = board.create('glider', [0, 0, line0], { name: 'b' });
var gl2 = board.create('glider', [1, -1, line1], { name: 'a' });

var line = board.create('line', [gl1, gl2]);

// offset determines the slope of line
var offset = gl2.Y() - gl1.Y();

// Drag gl1 and keep the slope of the line
gl1.on('drag', function() {
    gl2.moveTo([gl1.X(), gl1.Y() + offset]);
});

// Drag gl2 and adapt the slope of the line
gl2.on('drag', function() {
    offset = gl2.Y() - gl1.Y();
});

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.