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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

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ANSWER

[tex]|A'B'| = 5 \: units[/tex]



EXPLANATION

The formula for calculating the scale factor is


[tex]k = \frac{image \: length}{object \: length} [/tex]
Or

[tex]k = \frac{ |A'B'| }{ |AB|} [/tex]




Where k is the scale factor.



We were given
[tex] |A'B'|=10[/tex]


This is the image length.


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



[tex] \frac{1}{2} = \frac{ |A'B'| }{ 10} [/tex]
Multiply both sides by 10 to get,



[tex] \frac{1}{2}\times 10= |A'B'|[/tex]



[tex]|A'B'| = 5 \: units[/tex]

Answer:

Option (b) is correct.

The length of  A'B'  is 5 inches.

Step-by-step explanation:

Given : line segment AB is 10 inches long. AB is dilated to form A'B' with a scale factor of [tex]\frac{1}{2}[/tex]

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  [tex]\frac{1}{2}[/tex] which less than 1 , so line segment A'B' decreases.

New image = scaling factor × original image

that is A'B' = [tex]\frac{1}{2}\times 10=5[/tex]

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

Option (b) is correct.

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