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
∵ [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∵ A = [tex](x_{1},y_{1})[/tex] and B = [tex](x_{2},y_{2})[/tex]
∵ A = (1 , 4) and B = (4 , 8)
∴ [tex](x_{1},y_{1})=(1 , 4)[/tex] and [tex](x_{2},y_{2})=(4 , 8)[/tex]
∵ AB = [tex]\sqrt{(4-1)^{2}+(8-4)^{2}}=5[/tex]
∴ AB = 5 units
∵ A'B' = 4 AB
∴ A'B' = 4 × 5 = 20
∴ The length of the new segments A'B' is 20 units
