Question

problem 1 segment ab measures 3 cm. point o is the center of dilation. how long is the image of ab after a dilation with... a. scale factor 5? b. scale factor 3.7? c. scale factor 1/5? d. scale factor s?

Explanation:

Step1: Recall dilation formula

The length of the image of a segment after dilation is given by the product of the scale - factor and the length of the original segment. Let the length of the original segment $AB$ be $l_0 = 3$ cm and the scale - factor be $s$. The length of the image segment $l$ is $l=s\times l_0$.

Step2: Calculate lengths for each scale - factor

a. When $s = 5$

$l=5\times3=15$ cm

b. When $s = 3.7$

$l = 3.7\times3=11.1$ cm

c. When $s=\frac{1}{5}$

$l=\frac{1}{5}\times3 = 0.6$ cm

d. When $s$ is not given, we assume the general formula $l = s\times3$ cm

Answer:

a. 15 cm
b. 11.1 cm
c. 0.6 cm
d. $3s$ cm