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K-mean clustering algorithm has clustered the given $8$ observations into $3$ clusters after $1$st iteration as follows:

$C1: \: \{(3,3), (5,5), (7,7) \}$

$C2: \: \{(0,6), (6,0), (3,0) \}$

$C3: \: \{(8,8), (4,4)\}$

What will be the Manhattan distance for observation $(4,4)$ from cluster centroid $C1$ in the second iteration?

1. $2$
2. $\sqrt{2}$
3. $0$
4. $18$

Correct option: (1) 2

The new position of cluster centroid $C_1$ after the $1^{st}$ iteration will be $(\frac{1}{3}(3+5+7), \frac{1}{3}(3+5+7)) = (5, 5)$

The Manhattan distance between $(4,4)$ and $(5,5)$ is $|4 -5| + |4 - 5| = 2$

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