You can use slice() to make a copy then reverse() it

var newarray = array.slice().reverse();

var array = ['a', 'b', 'c', 'd', 'e'];
var newarray = array.slice().reverse();

console.log('a', array);
console.log('na', newarray);

Javascript has a reverse() method that you can call in an array

var a = [3,5,7,8];
a.reverse(); // 8 7 5 3

Not sure if that's what you mean by 'libraries you can't use', I'm guessing something to do with practice. If that's the case, you can implement your own version of .reverse()

function reverseArr(input) {
    var ret = new Array;
    for(var i = input.length-1; i >= 0; i--) {
        ret.push(input[i]);
    }
    return ret;
}

var a = [3,5,7,8]
var b = reverseArr(a);

Do note that the built-in .reverse() method operates on the original array, thus you don't need to reassign a.

You are making a new independent array, but you are not making independent copies of the items that fill your arrays. You need to do something like:

function reverseArr(input) {
    var ret = new Array;
    for(var i = input.length-1; i >= 0; i--) {
        ret.push({
            positionx: input[i].positionx, 
            positiony: input[i].positiony, 
            index: input[i].index
        });
    }

    return ret;
}

so that you are generating new objects (with the same properties) as well as the new array.