  We construct a family of compactifications of the affine cone of the
Grassmannian variety of 2-planes. We show that both the tropical variety of the
Pl\"ucker ideal and familiar valuations associated to the construction of
Newton-Okounkov bodies for the Grassmannian variety can be recovered from these
compactifications. In this way, we unite various perspectives for constructing
toric degenerations of flag varieties.
