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Shear transformation
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<iframe 
    src="https://jsxgraph.org/share/iframe/shear-transformation" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Shear transformation" 
    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';

    JXG.Options.label.autoPosition = true;
    JXG.Options.text.fontSize = 20;
    JXG.Options.line.strokeWidth = 1;
    
    var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 14, 14, -5], axis: true, keepaspectratio: true });
    
    var x = board.defaultAxes.x;
    var y = board.defaultAxes.y;
    
    var q = board.create('point', [2, 10], { name: 'q', snapToGrid: false });
    var q1 = board.create('point', [
            () => q.X() + q.Y(),
            () => q.Y()
        ], { name: 'φ(q)', color: 'blue' });
    
    var qx = board.create('point', [
            () => q.X(),
            () => 0
        ], { visible: false });
    
    var s1 = board.create('segment', [q, q1], { dash: 2 });
    var s2 = board.create('segment', [qx, q], { dash: 2 });
    var l1 = board.create('line', [q, qx], { visible: false });
    
    var r1 = board.create('line', [[0, 0], q], { straightFirst: false });
    
    var p = board.create('glider', [1, 3, r1], { name: 'p' });
    var p1 = board.create('point', [
            () => p.X() + p.Y(),
            () => p.Y()
        ], { name: 'φ(p)', color: 'blue' });
    
    var px = board.create('point', [
            () => p.X(),
            () => 0
        ], { visible: false });
    
    var r2 = board.create('line', [[0, 0], q1], { straightFirst: false });
    
    var s3 = board.create('segment', [p, p1], { dash: 2 });
    var s4 = board.create('segment', [px, p], { dash: 2 });
    
    board.create('hatch', [s1, 1]);
    board.create('hatch', [s2, 1]);
    
    board.create('hatch', [s3, 2]);
    board.create('hatch', [s4, 2]);
 </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!

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 20;
JXG.Options.line.strokeWidth = 1;

var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 14, 14, -5], axis: true, keepaspectratio: true });

var x = board.defaultAxes.x;
var y = board.defaultAxes.y;

var q = board.create('point', [2, 10], { name: 'q', snapToGrid: false });
var q1 = board.create('point', [
        () => q.X() + q.Y(),
        () => q.Y()
    ], { name: 'φ(q)', color: 'blue' });

var qx = board.create('point', [
        () => q.X(),
        () => 0
    ], { visible: false });

var s1 = board.create('segment', [q, q1], { dash: 2 });
var s2 = board.create('segment', [qx, q], { dash: 2 });
var l1 = board.create('line', [q, qx], { visible: false });

var r1 = board.create('line', [[0, 0], q], { straightFirst: false });

var p = board.create('glider', [1, 3, r1], { name: 'p' });
var p1 = board.create('point', [
        () => p.X() + p.Y(),
        () => p.Y()
    ], { name: 'φ(p)', color: 'blue' });

var px = board.create('point', [
        () => p.X(),
        () => 0
    ], { visible: false });

var r2 = board.create('line', [[0, 0], q1], { straightFirst: false });

var s3 = board.create('segment', [p, p1], { dash: 2 });
var s4 = board.create('segment', [px, p], { dash: 2 });

board.create('hatch', [s1, 1]);
board.create('hatch', [s2, 1]);

board.create('hatch', [s3, 2]);
board.create('hatch', [s4, 2]);
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Shear transformation" 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.
   */
   
   JXG.Options.label.autoPosition = true;
   JXG.Options.text.fontSize = 20;
   JXG.Options.line.strokeWidth = 1;
   
   var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 14, 14, -5], axis: true, keepaspectratio: true });
   
   var x = board.defaultAxes.x;
   var y = board.defaultAxes.y;
   
   var q = board.create('point', [2, 10], { name: 'q', snapToGrid: false });
   var q1 = board.create('point', [
           () => q.X() + q.Y(),
           () => q.Y()
       ], { name: 'φ(q)', color: 'blue' });
   
   var qx = board.create('point', [
           () => q.X(),
           () => 0
       ], { visible: false });
   
   var s1 = board.create('segment', [q, q1], { dash: 2 });
   var s2 = board.create('segment', [qx, q], { dash: 2 });
   var l1 = board.create('line', [q, qx], { visible: false });
   
   var r1 = board.create('line', [[0, 0], q], { straightFirst: false });
   
   var p = board.create('glider', [1, 3, r1], { name: 'p' });
   var p1 = board.create('point', [
           () => p.X() + p.Y(),
           () => p.Y()
       ], { name: 'φ(p)', color: 'blue' });
   
   var px = board.create('point', [
           () => p.X(),
           () => 0
       ], { visible: false });
   
   var r2 = board.create('line', [[0, 0], q1], { straightFirst: false });
   
   var s3 = board.create('segment', [p, p1], { dash: 2 });
   var s4 = board.create('segment', [px, p], { dash: 2 });
   
   board.create('hatch', [s1, 1]);
   board.create('hatch', [s2, 1]);
   
   board.create('hatch', [s3, 2]);
   board.create('hatch', [s4, 2]);
</jsxgraph>

Shear transformation

Geometry
$$\varphi: {\cal A}(\mathbb{R}^2) \to {\cal A}(\mathbb{R}^2), \; x \mapsto \begin{pmatrix}1 & 1 \\ 0& 1\end{pmatrix}$$ Points of the form ${x\choose \lambda}$ are mapped to: $$\varphi({x\choose \lambda}) = {x + \lambda\choose\lambda}$$
// Define the id of your board in BOARDID

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 20;
JXG.Options.line.strokeWidth = 1;

var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 14, 14, -5], axis: true, keepaspectratio: true });

var x = board.defaultAxes.x;
var y = board.defaultAxes.y;

var q = board.create('point', [2, 10], { name: 'q', snapToGrid: false });
var q1 = board.create('point', [
        () => q.X() + q.Y(),
        () => q.Y()
    ], { name: 'φ(q)', color: 'blue' });

var qx = board.create('point', [
        () => q.X(),
        () => 0
    ], { visible: false });

var s1 = board.create('segment', [q, q1], { dash: 2 });
var s2 = board.create('segment', [qx, q], { dash: 2 });
var l1 = board.create('line', [q, qx], { visible: false });

var r1 = board.create('line', [[0, 0], q], { straightFirst: false });

var p = board.create('glider', [1, 3, r1], { name: 'p' });
var p1 = board.create('point', [
        () => p.X() + p.Y(),
        () => p.Y()
    ], { name: 'φ(p)', color: 'blue' });

var px = board.create('point', [
        () => p.X(),
        () => 0
    ], { visible: false });

var r2 = board.create('line', [[0, 0], q1], { straightFirst: false });

var s3 = board.create('segment', [p, p1], { dash: 2 });
var s4 = board.create('segment', [px, p], { dash: 2 });

board.create('hatch', [s1, 1]);
board.create('hatch', [s2, 1]);

board.create('hatch', [s3, 2]);
board.create('hatch', [s4, 2]);

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.