Question

Rectangle A'B'C'D' is the image of rectangle ABCD after it has been translated according to the rule T–4, 3(x, y).

Which points are vertices of the pre-image, rectangle ABCD? Check all that apply.

(–1, –2)(7, 1)(–1, 7)(–1, 1)(7, –2)

Answer 1

Answer: A B D E

Step-by-step explanation: i just did it and i got it wrong so i got the answer

Answer 2

we know that

The rule of the translation of the pre-image to the image is equal to

`(x,y)-------> (x-4,y+3)`

that means

The translation is
`4` units to the left and
`3` units up

so

the inverse rule of translation of the image to the pre-image is equal to

`(x',y')-------> (x'+4,y'-3)`

we have the vertices of the image

`A'(-5,4)\\B'(3,4)\\C'(3,1)\\D'(-5,1)`

Applying the inverse rule of the translation find the coordinates of the vertices of the pre-image

Step 1

Find the coordinates of the vertex A of the pre-image

`(-5,4)-------> (-5+4,4-3)`

`(-5,4)-------> (-1,1)`

the coordinates of vertex A is
`(-1,1)`

Step 2

Find the coordinates of the vertex B of the pre-image

`(3,4)-------> (3+4,4-3)`

`(3,4)-------> (7,1)`

the coordinates of vertex B is
`(7,1)`

Step 3

Find the coordinates of the vertex C of the pre-image

`(3,1)-------> (3+4,1-3)`

`(3,1)-------> (7,-2)`

the coordinates of vertex C is
`(7,-2)`

Step 4

Find the coordinates of the vertex D of the pre-image

`(-5,1)-------> (-5+4,1-3)`

`(-5,1)-------> (-1,-2)`

the coordinates of vertex D is
`(-1,-2)`

Step 5

Verify which points are vertices of the pre-image

`(-1,-2)` -------> this point is the vertex D of the pre-image

`(7,1)` -------> this point is the vertex B of the pre-image

`(-1,7)` -------> this point is not a vertex of the pre-image

`(7,-2)` -------> this point is the vertex C of the pre-image

therefore

the answer is

`(-1,-2)`

`(7,1)`

`(7,-2)`