There are a few ways to do it.
You can run a loop that uses a LINQ query. It would check each item in the list and see if there are more than 1 of that item in the list. LINQ's version of Count() allows you to compare values.
bool HasDuplicates = false;
foreach (var item in MyList) {
    if (MyList.Count(i => i.x == item.x && i.y == item.y) > 1) {
        HasDuplicates = true;
        break;
    }
}
Or you can use Distinct() to make a second list that only has 1 of every value. Then compare the count of both lists. If the distinct one has a lower count, then there must be duplicates in the list.
var HasDuplicates = (MyList.Distinct().Count < MyList.Count)