In the case of the K$-$means algorithm, after the current iteration, we have $3$ centroids C$1$: $(1,1),$ C$2$: $(-2,1),$ and C$3$: $(2,-1).$ Currently, point A $(1,2)$ is assigned to the C$1$ cluster.

Will point A be assigned to the same cluster in the next iteration?

Assume that the current iteration is close to convergence.