Check out example codes for "flutter draw google map". It will help you in understanding the concepts better.

Code Example 1

import 'package:google_maps_flutter/google_maps_flutter.dart';

static const LatLng _center = const LatLng(33.738045, 73.084488);
final Set<Marker> _markers = {};
final Set<Polyline>_polyline={};

//add your lat and lng where you wants to draw polyline
LatLng _lastMapPosition = _center;
List<LatLng> latlng = List();
LatLng _new = LatLng(33.738045, 73.084488);
LatLng _news = LatLng(33.567997728, 72.635997456);

latlng.add(_new);
latlng.add(_news);

//call this method on button click that will draw a polyline and markers

void _onAddMarkerButtonPressed() {
    getDistanceTime();
    setState(() {
        _markers.add(Marker(
            // This marker id can be anything that uniquely identifies each marker.
            markerId: MarkerId(_lastMapPosition.toString()),
            //_lastMapPosition is any coordinate which should be your default 
            //position when map opens up
            position: _lastMapPosition,
            infoWindow: InfoWindow(
                title: 'Really cool place',
                snippet: '5 Star Rating',
            ),
            icon: BitmapDescriptor.defaultMarker,

        ));
        _polyline.add(Polyline(
            polylineId: PolylineId(_lastMapPosition.toString()),
            visible: true,
            //latlng is List<LatLng>
            points: latlng,
            color: Colors.blue,
        ));
    });

    //in your build widget method
    GoogleMap(
    //that needs a list<Polyline>
        polylines:_polyline,
        markers: _markers,
        onMapCreated: _onMapCreated,
        myLocationEnabled:true,
        onCameraMove: _onCameraMove,
        initialCameraPosition: CameraPosition(
            target: _center,
            zoom: 11.0,
        ),

        mapType: MapType.normal,

    );
}

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