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>
∵ ![d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
∵ A =
and B = ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
∵ A = (1 , 4) and B = (4 , 8)
∴
and ![(x_{2},y_{2})=(4 , 8)](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29%3D%284%20%2C%208%29)
∵ AB = ![\sqrt{(4-1)^{2}+(8-4)^{2}}=5](https://tex.z-dn.net/?f=%5Csqrt%7B%284-1%29%5E%7B2%7D%2B%288-4%29%5E%7B2%7D%7D%3D5)
∴ AB = 5 units
∵ A'B' = 4 AB
∴ A'B' = 4 × 5 = 20
∴ The length of the new segments A'B' is 20 units