The side lengths of triangle ABC are 10, 14, and 16. The side lengths of triangle A'B'C' are 35, 49, and 56. Identify the scale factor of a single dilation between the preimage ABC and image A'B'C'.
5.6
3.5
3
2/7
To find the scale factor between two similar triangles, we can compare the corresponding side lengths.
In this case, the corresponding side lengths are:
AC/A'C' = 10/35 = 2/7
AB/A'B' = 14/49 = 2/7
BC/B'C' = 16/56 = 2/7
Since all the ratios between corresponding side lengths are equal to 2/7, the scale factor of the dilation is 2/7. Therefore, the correct answer is 2/7.