Question

line segment uv is 12 cm long and dilated with a scale factor of 1.5. what is the difference between the lengths of uv and uv?

Explanation:

Step1: Find the length of the dilated line - segment

The length of the dilated line - segment is the original length times the scale factor. If the original length of line - segment $UV$ is $l = 12$ cm and the scale factor $k = 1.5$, then the length of the dilated line - segment $U'V'$ is $l'=l\times k$. So, $l'=12\times1.5 = 18$ cm.

Step2: Calculate the difference in lengths

The difference $\Delta l$ between the lengths of the dilated and the original line - segments is $\Delta l=l' - l$. Substitute $l' = 18$ cm and $l = 12$ cm into the formula: $\Delta l=18 - 12=6$ cm.

Answer:

6