Question

Which algebraic representation shows a dilation? (x, y) → (x+2, y+2) (x, y) → (2x, 2y) (x, y) → (y, -x) (x, y) → (-x, y)

Answer 1

(x,y) -> (2x,2y)

Answer 2

Option B:
`(x, y) \rightarrow(2 x, 2 y)` is the algebraic representation that shows dilation.

Step-by-step explanation:

From the options, we need to determine the algebraic representation that shows a dilation.

Option A:
`(x, y) \rightarrow(x+2, y+2)`

The translation shows that the graph is shifted 2 units to the left and 2 units up.

Thus, the translation is not dilation.

Hence, Option A is not the correct answer.

Option B:
`(x, y) \rightarrow(2 x, 2 y)`

The translation shows that the graph is enlarged or reduced by a factor of 2.

Since, the dilation of a transformation produces the same image but of different size.

Hence, the translation
`(x, y) \rightarrow(2 x, 2 y)` is dilation.

Hence, Option B is the correct answer.

Option C:
`(x, y) \rightarrow(y,-x)`

The translation
`(x, y) \rightarrow(y,-x)` is the rotation of the figure under 270° counterclockwise about the origin.

Thus, the translation is not dilation.

Hence, Option C is not the correct answer.

Option D:
`(x, y) \rightarrow(-x, y)`

The translation
`(x, y) \rightarrow(-x, y)` shows that the graph is reflected across the y - axis.

Thus, the translation is not dilation.

Hence, Option D is not the correct answer.