A dilation maps a segment of length $4$ units to a segment of length $8$ units. What is the scale factor of the dilation?

• A. $2$
• B. $8$
• C. $\frac{1}{2}$
• D. $4$

Answer: (A)

Verified step by step guidance

1. Identify the original length of the segment before dilation, which is given as 4 units.
2. Identify the new length of the segment after dilation, which is given as 8 units.
3. Recall that the scale factor of a dilation is the ratio of the image length to the original length.
4. Set up the ratio for the scale factor as \(\frac{\text{new length}}{\text{original length}}\) which becomes \(\frac{8}{4}\).
5. Simplify the fraction \(\frac{8}{4}\) to find the scale factor.