Answer:
Scale factor(k) defined as:
[tex]k = \frac{\text{Dilated image}}{\text{original image}}[/tex]
As per the statement:
The original length of AB is 9 centimeters.
A dilation with a scale factor of 2 is applied to AB.
⇒k = 2
We have to find the length of the image of AB after the dilation is applied.
Using definition of scale factor:
[tex]k = \frac{\text{Length of Dilated image AB}}{\text{Length of original image AB}}[/tex]
Substitute the given values we have;
[tex]2= \frac{\text{Length of Dilated image AB}}{9}[/tex]
Multiply both sides by 9 we have;
[tex]18 = \text{Length of image of AB}[/tex]
or
[tex]\text{Length of image of AB} =18[/tex]
therefore, the length of the image of AB after the dilation is applied. is, 18
