Question

Given: line segment AB is 10 inches long. Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 1 2 . A) 1 2 inches B) 5 inches C) 10 inches D) 20 inches

Answer 1

Option (b) is correct.

The length of A'B' is 5 inches.

Explanation:

Given : line segment AB is 10 inches long. AB is dilated to form A'B' with a scale factor of
`(1)/(2)`

we have to find the length of A'B'

Dilation of a figure is the increase or decrease in the length of the figure by a fixed scaling factor. if scaling factor is greater than 1 , then figure size increases, and if scaling factor is less than 1 , then figure size decreases.

Here, scaling factor is
`(1)/(2)` which less than 1 , so line segment A'B' decreases.

New image = scaling factor × original image

that is A'B' =
`(1)/(2)* 10=5`

Thus, the length of A'B' is 5 inches.

Option (b) is correct.

Answer 2

ANSWER


`|A'B'| = 5 \: units`



EXPLANATION

The formula for calculating the scale factor is



`k = (image \: length)/(object \: length)`
Or


`k = ( |A'B'| )/( |AB|)`




Where k is the scale factor.



We were given

`|A'B'|=10`


This is the image length.


We substitute the scale factor and the image length in to the formula to get,




`(1)/(2) = ( |A'B'| )/( 10)`
Multiply both sides by 10 to get,




`(1)/(2)* 10= |A'B'|`




`|A'B'| = 5 \: units`