I'm not really sure what you mean by the centroid matrix. Do you have 419 (x,y) coordinates of centroids? Or do you have only 2 centroids? Are the 419 points actually data points, not centroids? Did you use k = 2 to cluster those 419 data points into 2 clusters, each with a centroid so that you have 2 centroids, not 419?
Assuming 2 clusters and 419 training points, you can find a generalized distance which is like a z score which is the number of standard deviations away from the centroid. So a "big" cluster would have more "pull" on determining which cluster an arbitrary point belonged to than a "small" compact cluster. So just calculate the centroid and average distance from the centroid for the two clusters. Then do it for your arbitrary point and figure out which generalized distance is lower - that's the cluster your point belongs to (should be assigned to).
