Question

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

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation from \(\triangle ABC\) (pre - image) to \(\triangle DBE\) (image) is given by \(k=\frac{\text{length of a side in image}}{\text{length of the corresponding side in pre - image}}\).

Step2: Identify the corresponding sides

We are given \(AC = 16.12\) (side in pre - image \(\triangle ABC\)) and \(ED=12.09\) (side in image \(\triangle DBE\)).

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{ED}{AC}\).

$$k=\frac{12.09}{16.12}$$

$$k = 0.75$$

Answer:

B. 0.75