Based on the previous cluster assignment, we now calculate the new cluster centers \theta_{A,1} and \theta_{B,1}. What are the new coordinates of \theta_{A,1} and \theta_{B,1}? Make the steps in your computation explicit.
For P \in \left\{ A, B \right\}, we have
\begin{align*}
\theta_{P,1}
& = \frac{\sum_{i = 1}^{10} z^{(i)} \textbf{1} \left\{ C^{(i)}_0 = P \right\}}
{\sum_{i = 1}^{10} \textbf{1} \left\{ C^{(i)}_0 = P \right\}} .
\end{align*}
Thus,
\theta_{A, 1} = \left( 1.886, 1.528 \right) ,
\hspace{1cm}
\theta_{B, 1}= \left( 4.178; 3.778 \right) .