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)
Responses
3.5
3.5
3
3
27
Start Fraction 2 over 7 End Fraction
5.6
To find the scale factor, we need to compare the corresponding side lengths of the preimage ABC and the image A′B′C′.
The scale factor can be found by dividing the corresponding side lengths of the image by the corresponding side lengths of the preimage.
For example, the side length of AB is 10 and the corresponding side length of A' B' is 35. Dividing 35 by 10, we get a scale factor of 3.5.
Doing the same for the other pairs of corresponding side lengths, we find:
BC' / BC = 49 / 14 = 3.5
AC' / AC = 56 / 16 = 3.5
So the scale factor of a single dilation between the preimage ABC and image A'B'C' is 3.5.