Final answer:
The parliament representative assemblies impacted American colonists by establishing representative legislatures in the colonies, fostering direct representation, and influencing the later development of American constitutional government.
Step-by-step explanation:
The impact that the parliament representative assemblies had on American colonists was that they established representative legislatures in the colonies. These colonial assemblies initiated legislation, controlled the budget by voting on taxes and expenditures, and were instrumental in the development of the concept of direct representation, which contrasted with the British system of virtual representation. By asserting their right of self-governance and questioning the legitimacy of Parliament's laws that did not directly represent the colonists' interests, these actions contributed to the eventual drafting of state governments and the shaping of American political thought during the Revolutionary Era, which later influenced the Constitution-making process and the establishment of the United States as a nation with a system of checks and balances and divided powers between a legislature, executive, and judiciary.