To determine the scale factor used in the dilation of a line segment \( AB \) with the center of dilation at the origin, we need to know the coordinates of points \( A \) and \( B \) before and after the dilation.
However, since the question does not provide those coordinates, we can analyze the possible scale factors provided in the responses.
A dilation factor can be:
- Positive, which enlarges the object (scale factor greater than 1).
- Negative, which flips the object over the origin in addition to the scaling (negative scale factor).
- Less than 1 (but greater than 0), which reduces the size of the object.
Among the options provided:
- 1 is a scale factor that results in no change.
- 3 enlarges the size by 3 times.
- Start Fraction 1 over 3 End Fraction (or \(\frac{1}{3}\)) reduces the size to one-third.
- β3 enlarges the size by 3 times but flips it.
- βStart Fraction 1 over 3 End Fraction (or -\(\frac{1}{3}\)) reduces the size and flips it.
Since we do not have the specific context or coordinates for points \( A \) and \( B \), we cannot definitively identify a single scale factor from this information. If you have more details about the coordinates of points \( A \) and \( B \) before and after dilation, please provide them to calculate the scale factor accurately.
If you have a specific scenario or example in mind, please share it, and we'll determine the scale factor based on that information.