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

Question

asked Dec 25, 2021 144k views

2 Answers

Susu · Answer 1 · 2021-12-29T05:49:05+0000

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.