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Answer:
The length of the new segments A'B' is 20 units ⇒ answer C
Step-by-step explanation:
* <em>Lets revise the dilation</em>
- A dilation is a transformation that changes the size of a figure.
- It can become larger or smaller, but the shape of the figure does
not change.
- The scale factor, measures how much larger or smaller the image
will be
- If the scale factor greater than 1, then the image will be larger
- If the scale factor between 0 and 1, then the image will be smaller
* <em>Lets solve the problem</em>
- line segment AB whose endpoints are (1, 4) and (4, 8) is dilated by
a scale factor of 4 and centered at the origin
∵ The scale factor is 4 and it is greater than 1
- The length of the image of line segment AB will enlarged by the
scale factor 4
∴ A'B' = 4 AB
* <em>Lets find the length of AB by using the rule of the distance</em>
∵
∵ A = and B =
∵ A = (1 , 4) and B = (4 , 8)
∴ and
∵ AB =
∴ AB = 5 units
∵ A'B' = 4 AB
∴ A'B' = 4 × 5 = 20
∴ The length of the new segments A'B' is 20 units