Question

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

Answer 1

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

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

∵
`d=\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

∵ A =
`(x_(1),y_(1))` and B =
`(x_(2),y_(2))`

∵ A = (1 , 4) and B = (4 , 8)

∴
`(x_(1),y_(1))=(1 , 4)` and
`(x_(2),y_(2))=(4 , 8)`

∵ AB =
`\sqrt{(4-1)^(2)+(8-4)^(2)}=5`

∴ AB = 5 units

∵ A'B' = 4 AB

∴ A'B' = 4 × 5 = 20

∴ The length of the new segments A'B' is 20 units