Exercise 4.7.9

If we start with 5 clusters, then first, we combine the two closest clusters at $(0,0)$ and $(1,0)$, then we have:

• $k=4$, combine $(0,0)$ and $(1,0)$ into one cluster, $P_1=(0.5,0),P_2=(3,0),P_3=(0,4),P_4=(0,8)$
• $k=3$, combine $(0,0),(1,0),(3,0)$ into one cluster, $P_1=(\frac{4}{3},0),P_2=(0,4),P_3=(0,8)$
• $k=2$, combine $(0,4),(0,8)$ into one cluster, $P_1=(\frac{4}{3},0),P_2=(0,6)$