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'. (1 point)
5.6
3.5
3
2/7
To find the scale factor of a dilation between the preimage ABC and image A'B'C', we can compare corresponding side lengths.
The ratio of the corresponding side lengths between the two triangles will give us the scale factor.
The side lengths of triangle ABC are 10, 14, and 16.
The side lengths of triangle A'B'C' are 35, 49, and 56.
Comparing the corresponding side lengths, we have:
Side AB in preimage ABC : Side A'B' in image A'B'C' = 10:35
Side BC in preimage ABC : Side B'C' in image A'B'C' = 14:49
Side AC in preimage ABC : Side A'C' in image A'B'C' = 16:56
To simplify the ratios, we can divide each side length by their corresponding sides:
10/35 = 2/7
14/49 = 2/7
16/56 = 2/7
The ratios are all equal to 2/7.
Therefore, the scale factor of the dilation between the preimage ABC and image A'B'C' is 2/7.