Question

if an image of a triangle is congruent to the pre - image, what is the scale factor of the dilation?
0.1
\\(\frac{1}{2}\\)
1
10

Explanation:

Step1: Recall dilation and congruence

Dilation is a transformation that changes the size of a figure. If two figures are congruent, their corresponding sides are equal in length.

Step2: Relate scale factor to congruence

The scale factor \( k \) of a dilation determines the ratio of the length of the image to the pre - image. For a dilation with scale factor \( k \), the length of a side of the image \( l' \) is related to the length of the corresponding side of the pre - image \( l \) by the formula \( l'=k\times l \). If the image and pre - image are congruent, then \( l' = l \). Substituting into the formula \( l=k\times l \), dividing both sides by \( l \) (assuming \( l
eq0 \)), we get \( k = 1 \).

Answer:

C. 1 (assuming the options are labeled as A. 0.1, B. \(\frac{1}{2}\), C. 1, D. 10)