Suppose that the data mining task is to cluster points (with (x, y) representing location) into three clusters, where the points are

A1(2, 10), A2(2, 5), A3(8, 4), B1(5, 8), B2(7, 5), B3(6, 4), C1(1, 2), C2(4, 9).

The distance function is Euclidean distance. Suppose initially we assign A1, B1, and C1 as the center of each cluster, respectively. Run the k-means algorithm and show the clusters obtained during the first three iterations of the algorithm.

Please show all the work. Thanks.