Question

1. if segment ab was dilated by a scale factor of 1.5, what is the length of the image ab?
2. segment ab was dilated to create segment ab. what scale factor was used?
3. if segment ab was dilated by a scale factor of 4, what is the length of the image ab?
4. if segment ab was dilated by a scale factor of 1/2, what is the length of the image ab?

Explanation:

Step1: Recall the formula for dilation

The formula for dilation is \(A'B' = k\times AB\), where \(k\) is the scale factor.

Step2: Substitute the values for each problem

Problem 1

Given \(AB = 8\) and \(k = 1.5\).
Using the formula \(A'B'=k\times AB\), we substitute \(k = 1.5\) and \(AB = 8\)
\(A'B'=1.5\times8\)
\(A'B' = 12\)

Problem 2

Given \(AB = 18\) and \(A'B'=6\).
Using the formula \(k=\frac{A'B'}{AB}\), we substitute \(A'B' = 6\) and \(AB = 18\)
\(k=\frac{6}{18}=\frac{1}{3}\)

Problem 3

Given \(AB = 5\) and \(k = 4\).
Using the formula \(A'B'=k\times AB\), we substitute \(k = 4\) and \(AB = 5\)
\(A'B'=4\times5 = 20\)

Problem 4

Given \(AB = 6\) and \(k=\frac{1}{2}\).
Using the formula \(A'B'=k\times AB\), we substitute \(k=\frac{1}{2}\) and \(AB = 6\)
\(A'B'=\frac{1}{2}\times6=3\)

Answer:

1. \(12\)
2. \(\frac{1}{3}\)
3. \(20\)
4. \(3\)