# Why is the decision boundary for K-means clustering linear?

Apparently, for K-means clustering, the decision boundary for whether a data point lies in cluster $A$ or cluster $A'$ is linear.

I don't quite understand this statement. Why is it linear? Every iteration of K-means clustering, I reassign data points to clusters to minimize square error. Then, I reassign the prototypes (centers of the clusters) to minimize error again.

How do these processes create a "linear decision boundary"?