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Two reflections: parallel lines
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<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/two-reflections-i-parallel-lines" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Two reflections: parallel lines" 
    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,
            showClearTraces: true
        }),
        A = board.create('point', [-2, -2], { withLabel: false }),
        B = board.create('point', [3, -4], { withLabel: false }),
        C = board.create('point', [-2, 2], { withLabel: false }),
        s = board.create('line', [A, B], { name: 's', withLabel: true }),
        t = board.create('parallel', [s, C], { name: 't', withLabel: true }),
    
        Ss = board.create('transform', [s], { type: 'reflect' }),
        St = board.create('transform', [t], { type: 'reflect' }),
    
        P1 = board.create('point', [0, -3], { name: 'P_1', color: 'green', size: 8 }),
        P2 = board.create('point', [P1, Ss], { name: 'P_2', color: 'green' }),
        P3 = board.create('point', [P2, St], { name: 'P_3', color: 'green', trace: true }),
    
        Q1 = board.create('point', [1, -4], { name: 'Q_1', color: 'blue', size: 8 }),
        Q2 = board.create('point', [Q1, Ss], { name: 'Q_2', color: 'blue' }),
        Q3 = board.create('point', [Q2, St], { name: 'Q_3', color: 'blue', trace: true }),
    
        l1 = board.create('line', [P1, Q1], { color: 'black', strokeWidth: 1, dash: 2 }),
        l2 = board.create('line', [P2, Q2], { color: 'black', strokeWidth: 1, dash: 2 }),
        l3 = board.create('line', [P3, Q3], { color: 'black', strokeWidth: 1, dash: 2 }),
    
        g1 = board.create('segment', [P1, P2], { color: 'orange', strokeWidth: 1, dash: 3 }),
        g2 = board.create('segment', [P2, P3], { color: 'orange', strokeWidth: 1, dash: 3 }),
        h1 = board.create('segment', [Q1, Q2], { color: 'orange', strokeWidth: 1, dash: 3 }),
        h2 = board.create('segment', [Q2, Q3], { color: 'orange', strokeWidth: 1, dash: 3 });
 </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,
        showClearTraces: true
    }),
    A = board.create('point', [-2, -2], { withLabel: false }),
    B = board.create('point', [3, -4], { withLabel: false }),
    C = board.create('point', [-2, 2], { withLabel: false }),
    s = board.create('line', [A, B], { name: 's', withLabel: true }),
    t = board.create('parallel', [s, C], { name: 't', withLabel: true }),

    Ss = board.create('transform', [s], { type: 'reflect' }),
    St = board.create('transform', [t], { type: 'reflect' }),

    P1 = board.create('point', [0, -3], { name: 'P_1', color: 'green', size: 8 }),
    P2 = board.create('point', [P1, Ss], { name: 'P_2', color: 'green' }),
    P3 = board.create('point', [P2, St], { name: 'P_3', color: 'green', trace: true }),

    Q1 = board.create('point', [1, -4], { name: 'Q_1', color: 'blue', size: 8 }),
    Q2 = board.create('point', [Q1, Ss], { name: 'Q_2', color: 'blue' }),
    Q3 = board.create('point', [Q2, St], { name: 'Q_3', color: 'blue', trace: true }),

    l1 = board.create('line', [P1, Q1], { color: 'black', strokeWidth: 1, dash: 2 }),
    l2 = board.create('line', [P2, Q2], { color: 'black', strokeWidth: 1, dash: 2 }),
    l3 = board.create('line', [P3, Q3], { color: 'black', strokeWidth: 1, dash: 2 }),

    g1 = board.create('segment', [P1, P2], { color: 'orange', strokeWidth: 1, dash: 3 }),
    g2 = board.create('segment', [P2, P3], { color: 'orange', strokeWidth: 1, dash: 3 }),
    h1 = board.create('segment', [Q1, Q2], { color: 'orange', strokeWidth: 1, dash: 3 }),
    h2 = board.create('segment', [Q2, Q3], { color: 'orange', strokeWidth: 1, dash: 3 });
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Two reflections: parallel lines" 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,
           showClearTraces: true
       }),
       A = board.create('point', [-2, -2], { withLabel: false }),
       B = board.create('point', [3, -4], { withLabel: false }),
       C = board.create('point', [-2, 2], { withLabel: false }),
       s = board.create('line', [A, B], { name: 's', withLabel: true }),
       t = board.create('parallel', [s, C], { name: 't', withLabel: true }),
   
       Ss = board.create('transform', [s], { type: 'reflect' }),
       St = board.create('transform', [t], { type: 'reflect' }),
   
       P1 = board.create('point', [0, -3], { name: 'P_1', color: 'green', size: 8 }),
       P2 = board.create('point', [P1, Ss], { name: 'P_2', color: 'green' }),
       P3 = board.create('point', [P2, St], { name: 'P_3', color: 'green', trace: true }),
   
       Q1 = board.create('point', [1, -4], { name: 'Q_1', color: 'blue', size: 8 }),
       Q2 = board.create('point', [Q1, Ss], { name: 'Q_2', color: 'blue' }),
       Q3 = board.create('point', [Q2, St], { name: 'Q_3', color: 'blue', trace: true }),
   
       l1 = board.create('line', [P1, Q1], { color: 'black', strokeWidth: 1, dash: 2 }),
       l2 = board.create('line', [P2, Q2], { color: 'black', strokeWidth: 1, dash: 2 }),
       l3 = board.create('line', [P3, Q3], { color: 'black', strokeWidth: 1, dash: 2 }),
   
       g1 = board.create('segment', [P1, P2], { color: 'orange', strokeWidth: 1, dash: 3 }),
       g2 = board.create('segment', [P2, P3], { color: 'orange', strokeWidth: 1, dash: 3 }),
       h1 = board.create('segment', [Q1, Q2], { color: 'orange', strokeWidth: 1, dash: 3 }),
       h2 = board.create('segment', [Q2, Q3], { color: 'orange', strokeWidth: 1, dash: 3 });
</jsxgraph>

Two reflections: parallel lines

Euclidean
Geometry
This JSXGraph example shows reflections of points across two __parallel__ lines. Points ($P_1$ and $Q_1$) are mirrored successively on line $s$ and its parallel $t$, generating image points: $P_2$ and $Q_2$ are the mirror images from line reflection across line $s$. In turn, $P_3$ and $Q_3$ are the mirror images of reflecting these points across $t$. Lines and segments illustrate the transformation steps between original and reflected points. It can be observed that two reflections across two parallel lines result in a __translation__. To see this, move the defining point of line $t$.
Have also a look at the examples 
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        keepaspectratio: true,
        showClearTraces: true
    }),
    A = board.create('point', [-2, -2], { withLabel: false }),
    B = board.create('point', [3, -4], { withLabel: false }),
    C = board.create('point', [-2, 2], { withLabel: false }),
    s = board.create('line', [A, B], { name: 's', withLabel: true }),
    t = board.create('parallel', [s, C], { name: 't', withLabel: true }),

    Ss = board.create('transform', [s], { type: 'reflect' }),
    St = board.create('transform', [t], { type: 'reflect' }),

    P1 = board.create('point', [0, -3], { name: 'P_1', color: 'green', size: 8 }),
    P2 = board.create('point', [P1, Ss], { name: 'P_2', color: 'green' }),
    P3 = board.create('point', [P2, St], { name: 'P_3', color: 'green', trace: true }),

    Q1 = board.create('point', [1, -4], { name: 'Q_1', color: 'blue', size: 8 }),
    Q2 = board.create('point', [Q1, Ss], { name: 'Q_2', color: 'blue' }),
    Q3 = board.create('point', [Q2, St], { name: 'Q_3', color: 'blue', trace: true }),

    l1 = board.create('line', [P1, Q1], { color: 'black', strokeWidth: 1, dash: 2 }),
    l2 = board.create('line', [P2, Q2], { color: 'black', strokeWidth: 1, dash: 2 }),
    l3 = board.create('line', [P3, Q3], { color: 'black', strokeWidth: 1, dash: 2 }),

    g1 = board.create('segment', [P1, P2], { color: 'orange', strokeWidth: 1, dash: 3 }),
    g2 = board.create('segment', [P2, P3], { color: 'orange', strokeWidth: 1, dash: 3 }),
    h1 = board.create('segment', [Q1, Q2], { color: 'orange', strokeWidth: 1, dash: 3 }),
    h2 = board.create('segment', [Q2, Q3], { color: 'orange', strokeWidth: 1, dash: 3 });

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.