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

\[A_{1}(2,10), A_{2}(2,5), A_{3}(8,4), B_{1}(5,8), B_{2}(7,5), B_{3}(6,4), C_{1}(1,2), C_{2}(4,9) \text {. }\]

The distance function is Euclidean distance. Suppose initially we assign \(A_{1}, B_{1}\), and \(C_{1}\) as the center of each cluster, respectively. Use the \(k\)-means algorithm to show only

a. The three cluster centers after the first round of execution.

b. The final three clusters.