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. The original length of segment $AB$ is $l = 3$ cm.

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

Substitute $k=\frac{1}{5}$ and $l = 3$ into the formula $l'=k\times l$. So $l'=\frac{1}{5}\times3=\frac{3}{5}=0.6$ cm.

Step3: Calculate length for scale - factor $s$

Substitute $k = s$ and $l = 3$ into the formula $l'=k\times l$. So $l'=s\times3 = 3s$ cm.

Answer:

The length of the image of $AB$ after a dilation with a scale factor of $\frac{1}{5}$ is $0.6$ cm.
The length of the image of $AB$ after a dilation with a scale factor of $s$ is $3s$ cm.