Q$1.($K$-$means$)$ Use K$-$means algorithm and Euclidean distance to cluster the following $8$

examples into $3$ clusters: $1=(2,10),2=(2,5),3=(8,4),4=(5,8),5=(7,5),6=$

$(6,4),7=(1,2),8=(4,9).$ Suppose that the initial seeds $($centers of each cluster$)$ are p$1,$

p$4$ and p$7.$ Run the K$-$means algorithm for $1$ iteration only. At the end of this iteration show:

$1)$ The new clusters $($i$.$e$.,$ the examples belonging to each cluster$).$

$2)$ The centers of the new clusters.

$3)$ Do we need more iterations for convergence $($terminating the algorithm$)?$ Give your

$4)$ answer and brief explanation.