Question

Segment A B has a length of 4, segment A prime B prime has a length of 12. The distance from O to B is 3, and the distance from O to B prime is 9.
The diagram shows a dilation of segment AB. Which statements are true about the dilation? Select all that apply.
The dilation is an enlargement.
The dilation is a reduction.
Point O is the center of dilation.
The scale factor is 3.
The scale factor is 9.

Answer 1

Given the information provided, we can analyze the statements about the dilation of segment AB to segment A'B'.

1. **The dilation is an enlargement.**
- True. Since the length of segment A'B' (12) is greater than the length of segment AB (4), it indicates that the dilation has enlarged the segment.

2. **The dilation is a reduction.**
- False. A reduction would imply that the length of A'B' is less than that of AB, which is not the case here.

3. **Point O is the center of dilation.**
- True. The problem states that points B and B' are related through a dilation centered at point O.

4. **The scale factor is 3.**
- True. The scale factor can be calculated using the lengths of the segments. The length of A'B' is 12 and the length of AB is 4:
\[
\text{Scale factor} = \frac{\text{Length of A'B'}}{\text{Length of AB}} = \frac{12}{4} = 3.
\]

5. **The scale factor is 9.**
- False. As calculated previously, the scale factor is 3, not 9.

In summary, the true statements about the dilation are:
- The dilation is an enlargement.
- Point O is the center of dilation.
- The scale factor is 3.