The length of the image of the AB when dilated by a scale factor of 6 is [tex]24\sqrt{2}[/tex]
How to determine the length of the image of AB?
The coordinates are given as:
A = (-2,-5)
B = (2,-9)
The distance AB is calculated using:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]AB = \sqrt{(-2 - 2)^2 + (-5 + 9)^2}[/tex]
Evaluate
[tex]AB = \sqrt{32}[/tex]
Express as a root of 2
[tex]AB = 4\sqrt{2}[/tex]
The distance of the image is calculated using:
A'B = k* AB
Where k is the scale factor.
So, we have:
[tex]A'B' = 6 * 4\sqrt{2}[/tex]
This gives
[tex]A'B' = 24\sqrt{2}[/tex]
Hence, the length of the image of the AB is [tex]24\sqrt{2}[/tex]
Read more about dilation at:
https://brainly.com/question/3457976
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