Question

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 negative 6, 6, at E negative 3, 6, at F negative 1, 4, at G negative 3, 1, at H negative 6, 1, at I negative 8, 4, at D prime 1, negative 1, at E prime 4, negative 1, at F prime 6, negative 3, at G prime 4, negative 6, at H prime 1, negative 6, at I prime negative 1, negative 3 Which rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I'?

Answer 1

Answer:

$(x+7, y-7)$

Step-by-step explanation:

The rule of translation h unit horizontally shift and k unit vertically shift is given by:

$(x, y) \rightarrow (x+h, y+k)$

As per the statement:

From the given figure:

The vertices of the Hexagon DEFGHI are:

D(-6, 6), E(-3, 6), F(-1, 4), G(-3, 1), H(-6, 1) and I(-8, 4)

The  vertices of the Hexagon D'E'F'G'H'I' are:

D'(1, -1), E'(4, -1), F'(6, -3), G'(4, -6), H'(1, -6) and I'(-1, -3)

Using the rule of translation to find h and k:

Consider any vertices of DEFGHI

$D(-6, 6) \rightarrow D'(-6+h, 6+k)$

Given: D'(1, -1)

D'(-6+h, 6+k)  =D'(1, -1)

On comparing we have;

-6+h = 1 and 6+k = -1

⇒ h = 7  and k = -7

⇒Rule of translation we get, (x+7, y-7)

Therefore, the rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I' is:

$(x+7, y-7)$

Answer 2

(x,y)  is changed to (x+7,y-7)
It is translated 7 down and 4 to the right.