Question

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

a
a
a
a
6
6
6
6
b
b
b
b
a
a
a
a
?
12
9
2
b
b
b
b
a. find the value of x

Explanation:

Step1: Recall the formula for dilation

The formula for dilation is \( \text{Image length}=\text{Scale factor}\times\text{Original length}\).

Step2: Substitute the given values

Given the original length \(AB = 8\) and scale factor \(k=\frac{3}{2}\).
Using the formula \(A'B'=k\times AB\), substitute \(k = \frac{3}{2}\) and \(AB = 8\).
So \(A'B'=\frac{3}{2}\times8\).

Step3: Calculate the value

\(\frac{3}{2}\times8=\frac{3\times8}{2}=3\times4 = 12\).

Answer:

The length of the image \(A'B'\) is \(12\).