Answer :
The correct answer to the question "Judicial and legislative support of New York City's movement to govern itself is supported by" is:
Dillon's rule
Dillon's Rule is a principle of municipal law that states that a local government has only those powers that are explicitly granted to it by the state government. In the context of New York City's movement to govern itself, Dillon's Rule would mean that the city's authority to govern itself would be limited to what is specifically allowed by the state government. This rule has implications for the extent of autonomy and decision-making power that local governments, like New York City, have in managing their affairs.
In contrast, Home Rule refers to the ability of a city or county to set up its own system of self-government without receiving a charter from the state. This would provide New York City with more autonomy in decision-making compared to Dillon's Rule.
Cooley's Rule, on the other hand, is not directly related to the question at hand as it pertains to a different legal concept in constitutional law.
Constitutional Rule is a vague term that does not specifically address the relationship between New York City's movement for self-governance and judicial and legislative support.
Therefore, among the options provided, Dillon's Rule is the most relevant in understanding how New York City's movement to govern itself would be impacted by the legal framework governing its authority and powers.