Hexagon defghi is translated on the coordinate plane below to create hexagon d'e'f'g'h'i':
hexagon defghi and hexagon d prime e prime f prime g prime h prime i prime on the coordinate plane with ordered pairs at d are 3, 5, at e 7, 5, at f 8, 2, at g 7, negative 1, at h 3, negative 1, at i 2, 2; at d prime negative 6, 2, at e prime negative 2, 2, at f prime negative 1, negative 1, at g prime negative 2, negative 4, at h prime negative 6, negative 4, at i prime negative 7, negative 1
which rule represents the translation of hexagon defghi to hexagon d'e'f'g'h'i'?

(x, y)→(x − 9, y − 3)

Step-by-step explanation:

We have given Hexagon DEFGHI is translated on the coordinate plane to create hexagon D'E'F'G'H'I':

We write the translation one by one:

D (3, 5)

D' (-6, 2)

that translates to: (x - 9, y - 3), because that is for passing from D to D':

(3 - 9, 5 - 3) = (-6, 2)

Now for E (7,5)

E' (-2,2)

that translates to: (x - 9, y - 3), because that is for passing from E to E':

(7 - 9, 5 - 3) = (-2, 2)

Now for F(8,2)

F' (-1, -1)

that translates to: (x - 9, y - 3), because that is for passing from F to F':

(8 - 9, 2 - 3) = (-1, -1)

therefore if it is true for D and D', E and E', F and F' then it has to be true for all others for the rule to be true, so the  rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I' is (x, y)→(x − 9, y − 3)