Answer:
Scale factor(k) defined as:
\(k = \frac{\text{Dilated image}}{\text{original image}}\)
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:
\(k = \frac{\text{Length of Dilated image AB}}{\text{Length of original image AB}}\)
Substitute the given values we have;
\(2= \frac{\text{Length of Dilated image AB}}{9}\)
Multiply both sides by 9 we have;
\(18 = \text{Length of image of AB}\)
or
\(\text{Length of image of AB} =18\)
therefore, the length of the image of AB after the dilation is applied. is, 18
