Consider line segment ab whose endpoints are (1, 4) and (4, 8). if this segment is dilated by a scale factor of 4 centered at the origin, find the length of the new segment, a’b’.a. 4 b. 5 c.20 d. 400

The length of the new segments A'B' is 20 units ⇒ answer C

Step-by-step explanation:

* Lets revise the dilation

- 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

* Lets solve the problem

- 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

* Lets find the length of AB by using the rule of the distance

∵

∵ 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

its   c, f, a

step-by-step explanation:

hi there!

the answer is: 2 and -2

step-by-step explanation:

case 1: an absolute value of positive number will still be a positive number

so absolute value of 2 is 2

case 2: an absolute value of negative number will be positive number so absolute value of -2 is 2