$9.$ Assume that the K$-$means algorithm is employed in a clustering task using a Euclidean

distance between observations:

$($a$)$ Suppose the cluster centers for a given iteration of the algorithm are $1=(4,2)$ and

$2=(2,4).$ To which of the clusters would the observation x $=(2,2)$ be assigned?

Show your calculations.

$($b$)$ Suppose a cluster center is associated to the observations x$1=(5,3),$ x$2=(5,2),$ and

x$3=(3,1)$ after the assignment step. What would be the new position of this cluster

center after the movement step?