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

Answer:

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

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

∵ 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