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'
A. 5.6
B. 2/7
C. 3
D. 3.5
To find the scale factor of a dilation between two triangles, we need to compare the corresponding side lengths. We can do this by dividing the lengths of the corresponding sides of the image triangle A'B'C' by the corresponding side lengths of the preimage triangle ABC.
For side AB:
Scale factor = length of A'B' / length of AB = 35 / 10 = 3.5
For side AC:
Scale factor = length of A'C' / length of AC = 49 / 14 = 3.5
For side BC:
Scale factor = length of B'C' / length of BC = 56 / 16 = 3.5
The scale factor of a single dilation between triangle ABC and triangle A'B'C' is 3.5.
Therefore, the correct answer is D. 3.5