Draw a line between 2 divs once 2 consequence div clicked using angularjs

You might use lineTo from canvas context. See https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D for more details.

First, you define a canvas on html:

<canvas id="connection-canvas"></canvas>

Then you might draw a line on it:

function drawLine(p1, p2) {
  var canvas = document.getElementById("connection-canvas");
  var ctx = canvas.getContext("2d");

  ctx.beginPath();
  ctx.moveTo(p1.x, p1.y);
  ctx.lineTo(p2.x, p2.y);
  ctx.stroke();
}

All you need is to figure out the offset of your "round-pointers":

function getPoint(answerElement) {
    var roundPointer = answerElement.lastElementChild;

    return {
        y: answerElement.offsetTop + roundPointer.offsetTop + roundPointer.offsetHeight / 2,
        x: answerElement.offsetLeft + roundPointer.offsetLeft + roundPointer.offsetWidth / 2
    };
}

So you could with these two functions get the center point of a "round-pointer" and draw a line in canvas from it to another "round-pointer", assuming that the canvas is positioned on same answer-container's offset parent and its size must be large enough.

Next you have to deal with selecting the two answers to connect them. Below there is a demo for you. This demo does not handle erasing a line, if you change an answer.

var lastSelection;

// Add click listener for answer-container
function listenToClick() {
    var rows = document.querySelectorAll('.row'),
        row;
    var cols, col;

    for (row = 0; row < rows.length; row++) {
        cols = rows[row].children;

        for (col = 0; col < cols.length; col++) {
            // Bind information about which answer is this,
            // so we can prevent from connecting two answers on
            // same column.
            cols[col].addEventListener('click', selectAnswer.bind({
                row: row,
                col: col,
                element: cols[col]
            }));
        }
    }
}

// This is fired when a answer-container is clicked.
function selectAnswer(event) {
    if (lastSelection) {
        lastSelection.element.classList.remove('selected');
    }

    if (!lastSelection || lastSelection.col === this.col) {
        lastSelection = this;
        this.element.classList.add('selected');
    } else {
        drawLine(getPoint(this.element), getPoint(lastSelection.element));
        lastSelection = null;
    }
}

function getPoint(answerElement) {
    var roundPointer = answerElement.lastElementChild;

    return {
        y: answerElement.offsetTop + roundPointer.offsetTop + roundPointer.offsetHeight / 2,
        x: answerElement.offsetLeft + roundPointer.offsetLeft + roundPointer.offsetWidth / 2
    };
}

function drawLine(p1, p2) {
    var canvas = document.getElementById("connection-canvas");
    var ctx = canvas.getContext("2d");

    ctx.beginPath();
    ctx.moveTo(p1.x, p1.y);
    ctx.lineTo(p2.x, p2.y);
    ctx.stroke();
}

function resizeCanvas() {
    var canvas = document.getElementById("connection-canvas");
    var ctx = canvas.getContext("2d");

    ctx.canvas.width  = window.innerWidth;
    ctx.canvas.height = window.innerHeight;
}

listenToClick();
resizeCanvas();
.padding-answer-line-mapping
{
    padding-bottom:8px;
}

.answer-container
{
    width:40px;
    height:40px;
    background-color:#ccc;
    border:1px solid #ccc;
    margin:2px;
    float:left;
    text-align:center;
    padding-top:8px;
    cursor:pointer;
    position:relative;
}

.answer-container:hover, .answer-container:focus, .answer-container:active
{
    background-color: #0076e9;
    color: white;
    border: 1px solid #0076e9;
}

.round-pointer-right
{
    position: absolute;
    background-color:#ccc;
    cursor:pointer;
    width:10px;
    height:10px;
    border-radius: 50%;
    right:0px;
    top:14px;
    margin-right:-20px;
}

.round-pointer-left
{
    position: absolute;
    background-color:#ccc;
    cursor:pointer;
    width:10px;
    height:10px;
    border-radius: 50%;
    left:0px;
    top:14px;
    margin-left:-20px;
}

.selected {
    background-color: red;
}
<link href="//code.ionicframework.com/1.3.1/css/ionic.css" rel="stylesheet"/>
Match the following items.

 <canvas id="connection-canvas" style="position: absolute; top: 0; left: 0; right: 0; bottom: 0"></canvas>
<div class="row padding-answer-line-mapping">
    <div class="col answer-container">
        One
        <div class="round-pointer-right"></div>
    </div>
    <div class="col">
        
    </div>
    <div class="col answer-container">
        2
        <div class="round-pointer-left"></div>
    </div>
</div>
<div class="row padding-answer-line-mapping">
    <div class="col answer-container">
        Two
        <div class="round-pointer-right"></div>
    </div>
    <div class="col">
        
    </div>
    <div class="col answer-container">
        1
        <div class="round-pointer-left"></div>
    </div>
</div>

Here is a solution using SVG:

Once both left and right boxes clicked it will draw the line between the last two elements that clicked.

var leftEl, rightEl;
function drawLine(leftEl, rightEl) {
  var width = $(rightEl).offset().left - $(leftEl).offset().left;
  var height = $(leftEl).offset().top - $(rightEl).offset().top;
  if (height == 0) {
    height = 2;
  }
  var line = $("<div style='position: absolute; width: "+Math.abs(width)+"px; height: "+Math.abs(height)+"px;'><svg style='width: 100%; height: 100%;'><line x1='"+(height > 0 ? '0' : '100%')+"' y1='100%' ' x2='"+(height > 0 ? '100%' : '0')+"' y2='0' style='stroke:rgb(255,0,0);stroke-width:2'/></svg></div>");
  $('.container').append(line);
  myPos = height > 0 ? 'left bottom' : 'left top';
  ofPos = height == 2 ? 'center center-12' : 'left+5 top+5'
  
  if (leftEl.data('line')) {
    leftEl.data('line').remove()
  }
  if (rightEl.data('line')) {
    rightEl.data('line').remove()
  }
  
  line.position({
    my: myPos,
    at: ofPos,
    of: leftEl
  })
  
  leftEl.data('line', line)
  rightEl.data('line', line)
}

$('.box-left,.box-right').on('click', function() {
  if ($(this).hasClass('box-left')) {
    leftEl = this
  }
  if($(this).hasClass('box-right')) {
    rightEl = this
  }
  if (leftEl && rightEl) {
    drawLine(
      $(leftEl).parent().find('.round-pointer-right'),
      $(rightEl).parent().find('.round-pointer-left')
    );
    leftEl = rightEl = null;
  }
});
.container {
  position: relative;
}
.padding-answer-line-mapping
{
    padding-bottom:8px;
}

.answer-container
{
    width:40px;
    height:40px;
    background-color:#ccc;
    border:1px solid #ccc;
    margin:2px;
    float:left;
    text-align:center;
    padding-top:8px;
    cursor:pointer;
    position:relative;
}

.answer-container:hover, .answer-container:focus, .answer-container:active
{
    background-color: #0076e9;
    color: white;
    border: 1px solid #0076e9;
}

.round-pointer-right
{
    position: absolute;
    background-color:#ccc;
    cursor:pointer;
    width:10px;
    height:10px;
    border-radius: 50%;
    right:0px;
    top:14px;
    margin-right:-20px;
}

.round-pointer-left
{
    position: absolute;
    background-color:#ccc;
    cursor:pointer;
    width:10px;
    height:10px;
    border-radius: 50%;
    left:0px;
    top:14px;
    margin-left:-20px;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.css" />
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.js"></script>

<link href="http://code.ionicframework.com/1.3.1/css/ionic.css" rel="stylesheet"/>
Match the following items.

<div class="container">
<div class="row padding-answer-line-mapping">
    <div class="col answer-container box-left">
        One
        <div class="round-pointer-right"></div>
    </div>
    <div class="col">
        
    </div>
    <div class="col answer-container box-right">
        2
        <div class="round-pointer-left"></div>
    </div>
</div>
<div class="row padding-answer-line-mapping">
    <div class="col answer-container box-left">
        Two
        <div class="round-pointer-right"></div>
    </div>
    <div class="col">
        
    </div>
    <div class="col answer-container box-right">
        1
        <div class="round-pointer-left"></div>
    </div>
</div>
<div class="row padding-answer-line-mapping">
    <div class="col answer-container box-left">
        Three
        <div class="round-pointer-right"></div>
    </div>
    <div class="col">
        
    </div>
    <div class="col answer-container box-right">
        3
        <div class="round-pointer-left"></div>
    </div>
</div>
</div>

Update

I also added the option to remove a line once a box that already have a line was clicked again.