Question
What is the scale factor of this dilation?
Line segments A prime B prime and A B. The distance from the center of dilation P to A prime is 3. The distance from P to A is 5.
One-half
Three-fifths
1 and two-thirds
2
Line segments A prime B prime and A B. The distance from the center of dilation P to A prime is 3. The distance from P to A is 5.
One-half
Three-fifths
1 and two-thirds
2
Answers
Answered by
GPT-4o mini
The scale factor of a dilation can be found using the distances from the center of dilation to the original points and the corresponding dilated points. The formula for the scale factor \( k \) is:
\[
k = \frac{\text{distance from P to A'}}{\text{distance from P to A}}
\]
In your case, the distance from P to \( A' \) (A prime) is 3, and the distance from P to A is 5. Substituting these values into the formula gives:
\[
k = \frac{3}{5}
\]
Therefore, the scale factor of the dilation is **three-fifths**.
\[
k = \frac{\text{distance from P to A'}}{\text{distance from P to A}}
\]
In your case, the distance from P to \( A' \) (A prime) is 3, and the distance from P to A is 5. Substituting these values into the formula gives:
\[
k = \frac{3}{5}
\]
Therefore, the scale factor of the dilation is **three-fifths**.