Respuesta :

kudzordzifrancis

Answer:

[tex](x,y) \rightarrow ( \frac{1}{4} x, \frac{1}{4} y)[/tex]

Step-by-step explanation:

Quadrilateral BCDE has coordinates B(-8,4), C(0,4), D(8,8) and E(0,8).

Quadrilateral B'C'D'E' has coordinates B'(-2,1), C'(0,1), D'(2,2) and E'(0,2).

When we analyze the coordinates carefully, we realize that the coordinates of the preimage quadrilateral is multiplied by ¼ to obtain the coordinates of the image triangle.

Therefore the rule of the dilation is

[tex](x,y) \rightarrow ( \frac{1}{4} x, \frac{1}{4} y)[/tex]

The rule yields the dilation of the figure BCDE centered at the origin

[tex](x,y) -> (\frac{1}{4} x,\frac{1}{4} y)[/tex]

Option B is correct

Dilation :

Dilation is a transformation that changes the size of the figure .

Scale factor

Scale factor is the ratio of length of one side to the length of corresponding side.

From the given figure BCDE,

the length of DE= 8 units

The corresponding side D'E' = 2 units

The length of BC= 8 units

The corresponding side length B'C' = 2units

 [tex]scale \; factor =\frac{B'C'}{BC} =\frac{2}{8} =\frac{1}{4}[/tex]

To find out the rule, we multiple the scale factor for x  and y

The rule yields the dilation of the figure BCDE centered at the origin

[tex](x,y) -> (\frac{1}{4} x,\frac{1}{4} y)[/tex]

Learn more about the dilation here :

brainly.com/question/20482938

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