JSFiddle - React, Tailwind, and code Playground

JavaScript

var Point = [{

  "id": 1,
  "name": "A",
  "LastUpdate": "2016-07-08",
  "position": [36.8479648, 10.2793332]
}, {
  "id": 1,
  "name": "A",
  "LastUpdate": "2016-07-07",
  "position": [36.8791039, 10.2656209]
}, {
  "id": 1,
  "name": "A",
  "LastUpdate": "2016-07-09",
  "position": [36.9922751, 10.1255164]
}, {
  "id": 1,
  "name": "A",
  "LastUpdate": "2016-07-10",
  "position": [36.9009882, 10.3009531]
}, {
  "id": 1,
  "name": "A",
  "LastUpdate": "2016-07-04",
  "position": [37.2732415, 9.8713665]
}];

console.log(Point.sort(function(a, b) {
  return (new Date(b.LastUpdate)) - (new Date(a.LastUpdate))
}))