Suppose that you will use K$-$means algorithm to cluster the following dataset points $(2$ features$)$

into three clusters:

The distance function is Euclidean distance.

Let's assign point $1,4$ and $7$ as the initial centroid of each cluster, respectively. Please derive the

answer pf following two questions. Please use the Euclidean distance for your derivation.

$($a$)$ What are the centroids of three clusters after the first round of execution?

$($b$)$ What are the final three clusters?