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<!DOCTYPE html>
<html data-require="math graphie geom interactive">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>Translating Polygons</title>
    <script src="../khan-exercise.js"></script>
    <style type="text/css">
        #answer_area input[type=text] {
            width: 30px;
        }
    </style>
</head>
<body>
<div class="exercise">
    <div class="problems">
        <div id="drag">
            <div class="vars">
                <var id="SX,SY,EX,EY" data-ensure="SX !== EX || SY !== EY">randRange(-4, 4, 4)</var>
                <var id="DX,DY">[EX - SX, EY - SY]</var>
                <var id="POINTS">_.map(_.range(6), function() {
                    return {x: randRange(-4, 4), y: randRange(-4, 4)};
                })</var>
                <var id="HULL">_.map(Geom.convexhull(POINTS), function(p) {
                    return [p.x + SX, p.y + SY];
                })</var>
                <var id="TARGET"> _.map(HULL, function(p) {
                    return [p[0] + DX, p[1] + DY];
                })</var>
            </div>

            <p class="question">
                What is the image of the polygon below after the translation <code>T_{(<var>DX</var>, <var>DY</var>)}</code>?
            </p>

            <div class="problem">
                <div class="graphie" id="grid">
                    graphInit({
                        range: 11,
                        scale: 20,
                        axisArrows: "&lt;-&gt;",
                        tickStep: 1,
                        labelStep: 1,
                        gridOpacity: 0.05,
                        axisOpacity: 0.2,
                        tickOpacity: 0.4,
                        labelOpacity: 0.5
                    });

                    for (var i=0; i &lt; HULL.length; i++) {
                        line(HULL[i], HULL[(i+1) % HULL.length], { stroke: GRAY, strokeDasharray: "- " });
                    }

                    addMouseLayer();

                    graph.points = _.map(HULL, function(point) { return addMovablePoint({ coord: point, visible: false }); });
                    graph.lines = [];
                    for (var i=0; i &lt; graph.points.length; i++) {
                        graph.lines.push(addMovableLineSegment({ pointA: graph.points[i], pointZ: graph.points[(i+1) % graph.points.length], snapX: 1, snapY: 1}));
                    }

                    _.each(graph.lines, function(line) { line.onMove = function(dX, dY){ graph.updatePolygon(dX, dY); }});

                    graph.updatePolygon = function(dX, dY) {
                        _.each(graph.points, function(point){ point.setCoord([point.coord[0] + dX, point.coord[1] + dY]); point.updateLineEnds(); });
                        graph.curPoints = _.map(graph.points, function(point){ return point.coord; });
                    }

                    graph.showGuess = function() {
                        _.each(graph.points, function(point) { point.remove(); });
                        _.each(graph.lines, function(line) { line.remove(); });
                        graph.points = _.map(graph.curPoints, function(point) { return addMovablePoint({ coord: point, visible: false }); });
                        graph.lines = [];
                        for (var i=0; i &lt; graph.points.length; i++) {
                            graph.lines.push(addMovableLineSegment({ pointA: graph.points[i], pointZ: graph.points[(i+1) % graph.points.length], snapX: 1, snapY: 1}));
                        }
                    }

                    graph.drawAnswer = function() {
                        for (var i=0; i &lt; TARGET.length; i++) {
                            line(TARGET[i], TARGET[(i+1) % TARGET.length], { stroke: ORANGE });
                        }
                    }
                </div>
            </div>

            <div class="solution" data-type="custom">
                <div class="instruction">
                    Drag the blue polygon to its image under the given translation.
                </div>
                <div class="guess"> KhanUtil.currentGraph.graph.curPoints
                </div>
                <div class="validator-function">
                    coordList = _.map(KhanUtil.currentGraph.graph.points, function(point){ return point.coord; });
                    return _.all(coordList, function(point) {
                        return (point[0] === TARGET[_.indexOf(coordList, point)][0])
                            &amp;&amp; (point[1] === TARGET[_.indexOf(coordList, point)][1]);
                    });
                </div>
                <div class="show-guess">
                    KhanUtil.currentGraph.graph.curPoints = guess;
                    KhanUtil.currentGraph.graph.showGuess();
                </div>
            </div>

            <div class="hints">
                <p>
                    A translation <code>T_{(a, b)}</code> moves points <code>a</code> units in the <code>x</code> direction (right if
                    <code>a</code> is positive,left if <code>a</code> is negative) and
                    <code>b</code> units in the <code>y</code> direction (up if <code>b</code> is positive, down if <code>b</code> is negative).
                </p>
                <div>
                    To see where a translation moved this polygon, pick one point and translate it. For example, what happens to
                    <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> under this translation?
                    <div class="graphie" data-update="grid">
                        circle(HULL[0], { r: 0.2, fill: "black", stroke: "none" });
                    </div>
                    </br></br>
                </div>
                <div>
                    Under the translation <code>T_{(<var>DX</var>, <var>DY</var>)}</code>, <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> is translated to <code>(<var> TARGET[0][0] </var>,<var> TARGET[0][1] </var>)</code>. Where is the rest of the polygon translated?
                    <div class="graphie" data-update="grid">
                        circle(TARGET[0], { r: 0.2, fill: "black", stroke: "none" });
                        line(HULL[0], TARGET[0], { stroke: "black", arrows: "->"});
                    </div>
                    </br></br>
                </div>
                <div>
                    To get from <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> to <code>(<var> TARGET[0][0] </var>,<var> TARGET[0][1] </var>)</code>, we changed the x-coordinate by <var>DX</var> and the y-coordinate by <var>DY</var>. To translate the whole polygon, we need
                    to do the same thing to all of its points.
                </br></br>
                </div>
                <div>
                    The orange outline shows where the polygon ends up after the translation.
                    <div class="graphie" data-update="grid">
                        for (var i=0; i &lt; TARGET.length; i++) {
                            line(TARGET[i], TARGET[(i+1) % TARGET.length], { stroke: ORANGE });
                        }
                    </div>
                </div>
            </div>
        </div>
        <div id="reverse">
            <div class="vars">
                <var id="SX,SY,EX,EY" data-ensure="SX !== EX || SY !== EY">randRange(-4, 4, 4)</var>
                <var id="DX,DY">[EX - SX, EY - SY]</var>
                <var id="POINTS">_.map(_.range(6), function() {
                    return {x: randRange(-4, 4), y: randRange(-4, 4)};
                })</var>
                <var id="HULL">_.map(Geom.convexhull(POINTS), function(p) {
                    return [p.x + SX, p.y + SY];
                })</var>
                <var id="TARGET"> _.map(HULL, function(p) {
                    return [p[0] + DX, p[1] + DY];
                })</var>
            </div>

            <p class="question">
                What was the translation applied to move the blue solid shape to the orange dashed shape?
            </p>

            <div class="problem">
                <div class="graphie" id="grid">
                    graphInit({
                        range: 11,
                        scale: 20,
                        axisArrows: "&lt;-&gt;",
                        tickStep: 1,
                        labelStep: 1,
                        gridOpacity: 0.05,
                        axisOpacity: 0.2,
                        tickOpacity: 0.4,
                        labelOpacity: 0.5
                    });

                    for (var i=0; i &lt; HULL.length; i++) {
                        line(HULL[i], HULL[(i+1) % HULL.length], { stroke: BLUE });
                    }

                    for (var i=0; i &lt; TARGET.length; i++) {
                        line(TARGET[i], TARGET[(i+1) % TARGET.length], { stroke: ORANGE, strokeDasharray: "- " });
                    }

                </div>
            </div>

            <div class="solution" data-type="multiple"><code>{\LARGE T } \;(</code>
                <span class="sol" style="width:15px" data-fallback="1"><var>DX</var></span>
                <code>,</code>
                <span class="sol" style="width:15px" data-fallback="1"><var>DY</var></span>
                <code>)</code>
            </div>

            <div class="hints">
                <p>
                    A translation <code>T_{(a, b)}</code> moves points a units in the x direction (right if a is positive, left if a is negative) and
                    b units in the y direction (up if b is positive, down if b is negative).
                </p>
                <div>
                    To see what translation moved the blue polygon, pick one point and translate it. For example, what happened to
                    <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> under this translation?
                    <div class="graphie" data-update="grid">
                        circle(HULL[0], { r: 0.2, fill: "black", stroke: "none" });
                    </div>
                    </br></br>
                </div>
                <div>
                    Under this translation, <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> was translated to <code>(<var> TARGET[0][0] </var>,<var> TARGET[0][1] </var>)</code>. What does this tell you about the translation used?
                    <div class="graphie" data-update="grid">
                        circle(TARGET[0], { r: 0.2, fill: "black", stroke: "none" });
                        line(HULL[0], TARGET[0], { stroke: "black", arrows: "->"});
                    </div>
                    </br></br>
                </div>
                <div>
                    To get from <code>(<var> HULL[0][0] </var>,<var> HULL[0][1] </var>)</code> to <code>(<var> TARGET[0][0] </var>,<var> TARGET[0][1] </var>)</code>, we changed the x-coordinate by <var>DX</var> and the y-coordinate by <var>DY</var>.
                    </br></br>
                </div>
                <div>
                    The translation used was <code>T_{(<var>DX</var>, <var>DY</var>)}</code>.
                </div>
            </div>
        </div>
    </div>
</div>
</body>
</html>
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