Q:

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

Accepted Solution

A:
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]