How to draw the route between my current location and destination?

include this in your app build.gradle

dependencies {
    ...

    compile 'com.google.maps.android:android-maps-utils:0.4+'

}

This library has the class PolyUtil. I don’t know which Direction JSON parser you are using but I am pretty sure it will have a function that will return you the encoded polyline String. And then use the encoded string like below

public void drawPolyline (){
    String polylinePoints = YourParser.getPolylinePoints();
    List<LatLng> pointsList = PolyUtil.decode(points);
    mMap.addPolyline(new PolylineOptions().width(30).color(android.R.color.black).addAll(pointsList));

}

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