Which scale factors produce an expansion under a dilation of the original image? Select each correct answer.

Which scale factors will result in an expansion of the original image in a dilation process?

The scale factors that produce an expansion under a dilation of the original image are 2 and 0.75.

Dilation and Scale Factors

In a dilation transformation, the scale factor plays a crucial role in determining whether the image will expand or shrink. The scale factor is a multiplier that affects the dimensions of the original image. Expansion vs. Shrinkage: When the scale factor is greater than 1, it will result in an expansion of the original image. On the other hand, if the scale factor is between 0 and 1, it will lead to a shrinkage of the image. Correct Scale Factors for Expansion: Based on the provided options, the scale factors that produce an expansion under a dilation of the original image are 2 and 0.75. These scale factors will cause the image to increase in size. Explanation of Scale Factors: - When the scale factor is 2: This means that the image will be doubled in size. Each dimension of the original image will be multiplied by 2, resulting in a significant expansion. - When the scale factor is 0.75: This implies that the image will be reduced by 0.75 times its original size. Each dimension of the original image will be multiplied by 0.75, resulting in a smaller but still expanded representation. Incorrect Scale Factors for Expansion: The options -2, -0.75, and 0.75 will not result in an expansion of the original image. These scale factors fall within the range that leads to shrinkage, rather than expansion. Summary: In summary, the scale factors that produce an expansion under a dilation of the original image are 2 and 0.75. Therefore, options C and D are correct choices for this question.
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