In the below example I have created Drawing Polyline and Markers along the tapped position in Google Map. Polyline is a list of points where line segment are drawn between consecutive point. Here I have created fragment attribute in activity_main.xml and In AndroidMaindest.xml I have added permisson, In MainActivity I have used onMapClick method and OnClickListener method. You can see below example code it will clearly described you how to get Draw path between two locations.

Step(1)activity_main.xml layout-

 <RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context=".MainActivity" >

    <fragment
        android:id="@+id/map"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        class="com.google.android.gms.maps.SupportMapFragment"/>

</RelativeLayout>

Step(2)AndroidManifest.xml-

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
   
    android:versionCode="1"
    android:versionName="1.0" >
 
    <uses-sdk
        android:minSdkVersion="8"
        android:targetSdkVersion="17" />
 
    <permission
        android:name="in.wptrafficanalyzer.locationpolyline.permission.MAPS_RECEIVE"
        android:protectionLevel="signature"/>
 
    <uses-permission android:name="in.wptrafficanalyzer.locationpolyline.permission.MAPS_RECEIVE"/>
 
    <uses-permission android:name="android.permission.INTERNET"/>
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE"/>
    <uses-permission android:name="com.google.android.providers.gsf.permission.READ_GSERVICES"/>
    <uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"/>
    <uses-permission android:name="android.permission.ACCESS_FINE_LOCATION"/>
 
    <uses-feature
        android:glEsVersion="0x00020000"
        android:required="true"/>
 
    <application
        android:allowBackup="true"
        android:icon="@drawable/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >
 
        <activity
            android:name="in.wptrafficanalyzer.locationpolyline.MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />
                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
 
        <meta-data
            android:name="com.google.android.maps.v2.API_KEY"
            android:value="YOUR_API_KEY"/>
 
    </application>
</manifest>

Step(3)MainActivity-

public class MainActivity extends FragmentActivity {

    GoogleMap googleMap;
    ArrayList<LatLng> points;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        points = new ArrayList<LatLng>();

        // Getting reference to the SupportMapFragment of activity_main.xml
        SupportMapFragment fm = (SupportMapFragment) getSupportFragmentManager().findFragmentById(R.id.map);

        // Getting GoogleMap object from the fragment
        googleMap = fm.getMap();

        // Enabling MyLocation Layer of Google Map
        googleMap.setMyLocationEnabled(true);

        // Setting OnClick event listener for the Google Map
        googleMap.setOnMapClickListener(new OnMapClickListener() {

            @Override
            public void onMapClick(LatLng point) {

                // Instantiating the class MarkerOptions to plot marker on the map
                MarkerOptions markerOptions = new MarkerOptions();

                // Setting latitude and longitude of the marker position
                markerOptions.position(point);

                // Setting titile of the infowindow of the marker
                markerOptions.title("Position");

                // Setting the content of the infowindow of the marker
                markerOptions.snippet("Latitude:"+point.latitude+","+"Longitude:"+point.longitude);

                // Instantiating the class PolylineOptions to plot polyline in the map
                PolylineOptions polylineOptions = new PolylineOptions();

                // Setting the color of the polyline
                polylineOptions.color(Color.RED);

                // Setting the width of the polyline
                polylineOptions.width(3);

                // Adding the taped point to the ArrayList
                points.add(point);

                // Setting points of polyline
                polylineOptions.addAll(points);

                // Adding the polyline to the map
                googleMap.addPolyline(polylineOptions);

                // Adding the marker to the map
                googleMap.addMarker(markerOptions);

            }
        });

        googleMap.setOnMapLongClickListener(new OnMapLongClickListener() {

            @Override
            public void onMapLongClick(LatLng point) {
                // Clearing the markers and polylines in the google map
                googleMap.clear();

                // Empty the array list
                points.clear();
            }
        });
    }

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        // Inflate the menu; this adds items to the action bar if it is present.
        getMenuInflater().inflate(R.menu.main, menu);
        return true;
    }
}