Question

in the diagram, \\( \triangle abc \\) and \\( \triangle dbe \\) are similar. what is the scale factor of the dilation that will map the preimage \\( \triangle abc \\) onto the image \\( \triangle dbe \\)?
a. 1.33
b. 0.75
c. 0.66
d. 0.55

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\)

Step2: Identify the corresponding segments

Since \(\triangle ABC\sim\triangle DBE\), and \(AC = 16.12\) (pre - image segment) and \(ED=12.09\) (image segment)
\(k=\frac{ED}{AC}\)

Step3: Calculate the scale factor

\(k=\frac{12.09}{16.12}\)
\(k = 0.75\)

Answer:

B. 0.75