Question

The length of ​ AB¯¯¯¯¯ ​ is 10 inches. A dilation with a scale factor of 25 is applied. What is the length of the image of ​ AB¯¯¯¯¯ ​ ?

Answer 1

The answer is 4.

I hope this helps. :)

Answer 2

length of image of AB is 4 inches.

Explanation:

Scale factor(k) is defined as the ratio of image to the pre-image.

i.e,

`k = \frac{\text{Image}}{\text{Pre-image}}`

as per the statement:

The length of ​ AB ​ is 10 inches. A dilation with a scale factor of
`(2)/(5)`

⇒
`k= (2)/(5) =0.4` and Length of pre-image AB = 10 inches.

by definition of scale factor:

`\text{length of image AB} = k \cdot \text{Length of Pre-image AB}`

Substitute the given values we have;

`\text{length of image AB} = 0.4 \cdot 10`

Simplify:

`\text{length of image AB} =4` inches.

Therefore, the length of image AB is 4 inches.