'vaguely-formed' originates from the Latin word 'vagus,' meaning 'wandering' or 'indeterminate,' combined with the English word 'form,' which comes from the Latin 'forma,' meaning 'shape.'

'vagus' transformed into the Old French word 'vague,' and eventually became the modern English word 'vague.' The word 'form' has remained relatively unchanged from its Latin origins.

Initially, 'vague' meant 'wandering' or 'indeterminate,' but over time it evolved into its current meaning of 'not clearly defined.'