public class AppPoisModel
    {
        public int idPoiType { get; set; }
        public string sector { get; set; }
        public double latPoint { get; set; }
        public double lngPoint { get; set; }
    }

var result = (from c in db.coord
                      select new AppPoisModel
                      {
                          idPoiType = c.id,
                          sector = c.sector,
                          latPoint = c.latitude ?? 0,
                          lngPoint = c.longitude ?? 0
                      }).ToList();

[
{
    "$id": "1",
    "sector" : "A",
    "latPoint": 0,
    "lngPoint": 0
},
{
    "$id": "2",
    "sector" : "A",
    "latPoint": 0,
    "lngPoint": 0
}
]

[
{
    "$id": "1",
    "sector" : "A",
    "coords": [{latPoint, lngPoint}, {latPoint, lngPoint}]
}
]