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.