When did New York become an English colony

The territory from the Dutch king gave it to his brother the Duke of York.

English colonel Richard Nicolls captured it for his king  that named the colony after his brother.

Explanation:

In 1765 a congress of nine colonies was formed in New York, in which the leaders of these colonies allied themselves to take action against Britain, and in May 1775, the colonial leaders called on the people to prepare for the struggle against the occupiers.

answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.

step-by-step explanation:

there are three triangles, and three unknowns: x, y=length of middle segment, and z=cos(angles marked with red arc).

we need

and law of cosines,

the three equations are

see attached image for solution.

basic principles: federalism, separation of powers, checks and balances, judicial review, representative democracy, limited government, rule of law, individual rights and responsibilities, consent of the governed, majority rule, popular sovereignty, equal protection.