Nonetheless, seemingly different similarity measures may be equivalent after some transformation. Suppose we

have the following two$-$dimensional data set: $(10$ pt $)$

Consider the data as two$-$dimensional data points. Given a new data point, $x=(1\mathrm{.}4,1\mathrm{.}6)$ as a query, rank the

database points based on similarity with the query using Euclidean distance, Manhattan distance, supremum

distance, and cosine similarity. $($similar data points rank first$)$