Question

darius uses a computer graphics program to dilate a two - dimensional figure by a factor of 3. which statement is true? a) the area of the figure will increase by 3 square inches. b) the area of the figure will increase by 9 square inches. c) the area of the figure will increase by a factor of 3. d) the area of the figure will increase by a factor of 9.

Explanation:

Step1: Recall area - dilation relationship

For a two - dimensional figure, if the linear dimensions are dilated by a factor of $k$, the area of the figure is dilated by a factor of $k^{2}$.

Step2: Identify the dilation factor

Here, the dilation factor $k = 3$.

Step3: Calculate the area - dilation factor

The area of the figure will be dilated by a factor of $k^{2}=3^{2}=9$.

Answer:

D. The area of the figure will increase by a factor of 9.