Google Maps API V3 : How show the direction from a point A to point B (Blue line)?

Use directions service of Google Maps API v3. It's basically the same as directions API, but nicely packed in Google Maps API which also provides convenient way to easily render the route on the map.

Information and examples about rendering the directions route on the map can be found in rendering directions section of Google Maps API v3 documentation.

Using Javascript

I created a working demo that shows how to use the Google Maps API Directions Service in Javascript through a

• DirectionsService object to send and receive direction requests
• DirectionsRenderer object to render the returned route on the map

function initMap() {
  var pointA = new google.maps.LatLng(51.7519, -1.2578),
    pointB = new google.maps.LatLng(50.8429, -0.1313),
    myOptions = {
      zoom: 7,
      center: pointA
    },
    map = new google.maps.Map(document.getElementById('map-canvas'), myOptions),
    // Instantiate a directions service.
    directionsService = new google.maps.DirectionsService,
    directionsDisplay = new google.maps.DirectionsRenderer({
      map: map
    }),
    markerA = new google.maps.Marker({
      position: pointA,
      title: "point A",
      label: "A",
      map: map
    }),
    markerB = new google.maps.Marker({
      position: pointB,
      title: "point B",
      label: "B",
      map: map
    });

  // get route from A to B
  calculateAndDisplayRoute(directionsService, directionsDisplay, pointA, pointB);

}



function calculateAndDisplayRoute(directionsService, directionsDisplay, pointA, pointB) {
  directionsService.route({
    origin: pointA,
    destination: pointB,
    travelMode: google.maps.TravelMode.DRIVING
  }, function(response, status) {
    if (status == google.maps.DirectionsStatus.OK) {
      directionsDisplay.setDirections(response);
    } else {
      window.alert('Directions request failed due to ' + status);
    }
  });
}

initMap();

    html,
    body {
      height: 100%;
      margin: 0;
      padding: 0;
    }
    #map-canvas {
      height: 100%;
      width: 100%;
    }

<script src="https://maps.googleapis.com/maps/api/js?sensor=false"></script>

<div id="map-canvas"></div>

Also on Jsfiddle: http://jsfiddle.net/user2314737/u9no8te4/

Using Google Maps Web Services

You can use the Web Services using an API_KEY issuing a request like this:

https://maps.googleapis.com/maps/api/directions/json?origin=Toronto&destination=Montreal&key=API_KEY

An API_KEY can be obtained in the Google Developer Console with a quota of 2,500 free requests/day.

A request can return JSON or XML results that can be used to draw a path on a map.

Official documentation for Web Services using the Google Maps Directions API are here

In your case here is a implementation using directions service.

function displayRoute() {

    var start = new google.maps.LatLng(28.694004, 77.110291);
    var end = new google.maps.LatLng(28.72082, 77.107241);

    var directionsDisplay = new google.maps.DirectionsRenderer();// also, constructor can get "DirectionsRendererOptions" object
    directionsDisplay.setMap(map); // map should be already initialized.

    var request = {
        origin : start,
        destination : end,
        travelMode : google.maps.TravelMode.DRIVING
    };
    var directionsService = new google.maps.DirectionsService(); 
    directionsService.route(request, function(response, status) {
        if (status == google.maps.DirectionsStatus.OK) {
            directionsDisplay.setDirections(response);
        }
    });
}

  // First Initiate your map. Tie it to some ID in the HTML eg. 'MyMapID'
  var map = new google.maps.Map(
    document.getElementById('MyMapID'),
    {
      center: {
        lat: Some.latitude,
        lng: Some.longitude
      }
    }
  );
  // Create a new directionsService object.
  var directionsService = new google.maps.DirectionsService;
    directionsService.route({
      origin: origin.latitude +','+ origin.longitude,
      destination: destination.latitude +','+ destination.longitude,
      travelMode: 'DRIVING',
    }, function(response, status) {
      if (status === google.maps.DirectionsStatus.OK) {
        var directionsDisplay = new google.maps.DirectionsRenderer({
          suppressMarkers: true,
          map: map,
          directions: response,
          draggable: false,
          suppressPolylines: true, 
          // IF YOU SET `suppressPolylines` TO FALSE, THE LINE WILL BE
          // AUTOMATICALLY DRAWN FOR YOU.
        });

        // IF YOU WISH TO APPLY USER ACTIONS TO YOUR LINE YOU NEED TO CREATE A 
        // `polyLine` OBJECT BY LOOPING THROUGH THE RESPONSE ROUTES AND CREATING A 
        // LIST
        pathPoints = response.routes[0].overview_path.map(function (location) {
          return {lat: location.lat(), lng: location.lng()};
        });

        var assumedPath = new google.maps.Polyline({
         path: pathPoints, //APPLY LIST TO PATH
         geodesic: true,
         strokeColor: '#708090',
         strokeOpacity: 0.7,
         strokeWeight: 2.5
       });

       assumedPath.setMap(map); // Set the path object to the map

Use the directions API.

Make an ajax call i.e.

https://maps.googleapis.com/maps/api/directions/json?parameters

and then parse the responce