Option B: is the algebraic representation that shows dilation.
Explanation:
From the options, we need to determine the algebraic representation that shows a dilation.
<u>Option A:</u>
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.
<u>Option B:</u>
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 is dilation.
Hence, Option B is the correct answer.
<u>Option C:</u>
The translation 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.
<u>Option D</u>:
The translation shows that the graph is reflected across the y - axis.
Thus, the translation is not dilation.
Hence, Option D is not the correct answer.