Question

blems 1 - 2
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

Length of dilated segment = Original length × Scale - factor

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

Let the original length of segment $AB$ be $l = 3$ cm and scale - factor $k=\frac{1}{5}$. Then the length of the dilated segment $l_{1}=3\times\frac{1}{5}=\frac{3}{5}=0.6$ cm.

Step3: Calculate for scale - factor $s$

If the scale - factor is $s$ and the original length of segment $AB$ is $3$ cm, then the length of the dilated segment $l_{2}=3\times s = 3s$ cm.

Answer:

1. $0.6$ cm
2. $3s$ cm