Consider the following datapoints: $x_1=(2,10),x_2=(2,5),y_1=(5,8),y_2=$

$(7,5),z_1=(1,2),z_2=(4,9).$ We wish to perform $k-$means clustering with a Eu$-$

clidean distance metric on this data with $k=3.$ The initial centroids are chosen to

be $x_1,y_1,z_1.$ Given this, write down all steps of the algorithm until convergence.

Yor answer should include distance calculations, as well as any updates to the

centroids and the labelling of datapoints to their clusters.