Calculating new centroids when the centroids are chosen at random

When given two random points which are not instances in the dataset should I include the centroids in my calculations for the new centroids?

For example in this link they are using the starting centroids which are apart of the dataset to calculate the mean for the new centroids.

But if given random x and y coordinates lets say [2,1] and [3,2] which are not apart of the dataset do I also include them or just the instances in the set which have been clustered to those centroids in the mean calculation?