Question about K$-$means clustering

K$-$means clustering algorithm aims to partition n observations into k clusters in which each observation

belongs to one cluster. The algorithm is defined as follows.

$$ Step $1$: Choose the number of clusters k$.$

$$ Step $2$: Select k random points from the data to be the initial centroids or cluster centers.

$$ Step $3$: Assign each data point to the closest cluster centroid based on the distance

$$ Step $4$: Recompute the centroids of newly formed clusters using the new cluster memberships. Use

arithmetic mean for each dimension.

$$ Step $5$: Repeat steps $3$ and $4$ until a convergence is met

$10$p $5$

The table below shows the unlabeled data points in our dataset. Let k $=2$ and find two clusters by

taking initial centroids as points $5$ and $6.$ Clearly show all iterations and the final cluster points. Use

the Manhattan distance d$($x$,$ y$)=$ Sx$1$ x$2$S $+$ Sy$1$ y$2$S$.$