Question

segment $ab$ measures 3 centimeters. point $o$ is the center of dilation. how long is the image of $ab$ after a dilation with a scale factor of $\frac{1}{5}$? how long is the image of $ab$ after a dilation with a scale factor of $s$?

Explanation:

Step1: Recall dilation formula

The length of the dilated segment $l'$ is given by $l' = k\times l$, where $k$ is the scale - factor and $l$ is the original length. Here, $l = 3$ cm.

Step2: Calculate for scale factor $\frac{1}{5}$

When $k=\frac{1}{5}$, we substitute $l = 3$ cm into the formula $l'=k\times l$. So $l'=\frac{1}{5}\times3=\frac{3}{5}=0.6$ cm.

Step3: Calculate for scale factor $s$

When the scale - factor is $s$, using the formula $l' = k\times l$ with $l = 3$ cm, we get $l'=s\times3 = 3s$ cm.

Answer:

0.6 cm
3s cm