Question

segment ab is 3 centimeters long. point o is the center of dilation. how long is the image of segment ab after a dilation with a scale factor of 5? how long is the image of segment ab after a dilation with a scale factor of 3.7?

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 length for scale factor 5

For $k = 5$, we substitute into the formula: $l_1'=5\times3$.
$l_1' = 15$ cm.

Step3: Calculate length for scale factor 3.7

For $k = 3.7$, we substitute into the formula: $l_2'=3.7\times3$.
$l_2'=11.1$ cm.

Answer:

15 cm
11.1 cm