In array of coordinates find the point closest to the given

There's a Haversine formula to calculate spherical distance between your point and each point in array, e.g. using Array.prototype.reduce():

const haversine = ({longitude: lonA, latitude: latA}, {longitude: lonB, latitude: latB}) => {
        const {PI, sin, cos, atan2} = Math,
              r = PI/180,
              R = 6371,
              deltaLat = (latB - latA)*r,
              deltaLon = (lonB - lonA)*r,
              a = sin(deltaLat / 2)**2 + cos(cos(latB*r)*latA*r) * sin(deltaLon /2)**2,
              c = 2 * atan2(a**0.5, (1 - a)**0.5),
              d = R * c
        return d
      },
      
      obj = {latitude: 55.87, longitude: 4.20},

      arr = [{"latitude":55.85,"longitude":4.22},{"latitude":55.89,"longitude":4.16},{"latitude":55.88,"longitude":-4.24}],
      
      {closest} = arr.reduce((r,o) => {
        const distance = haversine(o, obj)
        distance < r.minDistance || !r.closest &&
        (r.closest = o, r.minDistance = distance)
        return r
      }, {closest: null, minDistance: null})
      
console.log(closest)

.as-console-wrapper{min-height:100%;}

You can do this with JS. You can use this piece of code

export class ContentComponent implements OnInit {

  compareTo: any = { latitude: 55.87, longitude: 4.20 };
  data: Array<any> = [
    {
      "latitude": 55.85,
      "longitude": 4.22
    },
    {
      "latitude": 55.89,
      "longitude": 4.16
    },
    {
      "latitude": 55.88,
      "longitude": -4.24
    }
  ];

  // data filtered
  filteredData: Array<any> = [];

  constructor() { }

  ngOnInit() {
    
    var tmpData: Array<any> = [];

    this.data.forEach(x => {
      var res = this.computeDistance(x.latitude, x.longitude, this.compareTo.latitude, this.compareTo.longitude, "K");
      tmpData.push({ distance: res, obj: x });
    });

    tmpData.sort((a, b) => a.distance - b.distance);
    tmpData.forEach(x => this.filteredData.push(x.obj));
    
  }

  computeDistance(lat1, lon1, lat2, lon2, unit) {
    if ((lat1 == lat2) && (lon1 == lon2)) {
      return 0;
    }
    else {
      var radlat1 = Math.PI * lat1/180;
      var radlat2 = Math.PI * lat2/180;
      var theta = lon1-lon2;
      var radtheta = Math.PI * theta/180;
      var dist = Math.sin(radlat1) * Math.sin(radlat2) + Math.cos(radlat1) * Math.cos(radlat2) * Math.cos(radtheta);
      if (dist > 1) {
        dist = 1;
      }
      dist = Math.acos(dist);
      dist = dist * 180/Math.PI;
      dist = dist * 60 * 1.1515;
      if (unit=="K") { dist = dist * 1.609344 }
      if (unit=="N") { dist = dist * 0.8684 }
      return dist;
    }
  }
}

Use below code to get the index. I follow the same pattern as followed by @Meadow.

let points = [{
        "latitude": 55.85,
        "longitude": 4.22
      },
      {
        "latitude": 55.89,
        "longitude": 4.16
      },
      {
        "latitude": 55.88,
        "longitude": -4.24
      },
      {
        "latitude": 55.86,
        "longitude": 4.21
      }
    ];
    let allDistance:any = [];

    points.forEach((x,index)=> {
      var res = this.getDistance(x.latitude, x.longitude, 55.87, 4.20, "km");
      allDistance.push({ distance: res, obj: x,index: index});
    });

    allDistance.sort((a, b) => a.distance - b.distance);
    console.log("Index:"+allDistance[0].index);  
    console.log(allDistance);   

Get Distance method:

  getDistance(markerLat: any, markerLon: any, sourceLat: any, sourceLng: any,unit): any {
    var radlat1 = Math.PI * sourceLat / 180;
    var radlat2 = Math.PI * markerLat / 180;
    var theta = sourceLng - markerLon;
    var radtheta = Math.PI * theta / 180;
    var dist = Math.sin(radlat1) * Math.sin(radlat2) + Math.cos(radlat1) * Math.cos(radlat2) * Math.cos(radtheta);
    if (dist > 1) {
      dist = 1;
    }
    dist = Math.acos(dist);
    dist = dist * 180 / Math.PI;
    dist = dist * 60 * 1.1515;
    dist = dist * 1.609344;
    if (unit != 'mi') {
      return isNaN(dist) ? 0 : dist;
    }
    return isNaN(dist * 0.62137) ? 0 : dist * 0.62137;
  }