Consider the following data points in a 2D space: (2, 1), (3, 1), (1, 2), (1, 4), (3, 3), (4, 5), (5, 5), (5, 6), (6, 4), and (8, 7). You are to apply the k-Means algorithm to this data set for k= 2. Assume that the points in boldface print are the initial centroids. Required:
Show the point assignment (i. e. which cluster each point is assigned to), the centroid coordinate, and the MSE after one iteration of the algorithm (i. e. a single cycle involving point assignment and centroid adjustment).