**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**