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
27
Start Fraction 2 over 7 End Fraction
5.6
5.6
3.5
3.5
3
To find the scale factor of a single dilation between triangle ABC and triangle A'B'C', we need to compare the corresponding side lengths.
The scale factor can be found by dividing the side lengths of the image triangle by the side lengths of the preimage triangle.
For example, if we compare side AB (length 10) of triangle ABC to side A'B' (length 35) of triangle A'B'C', we get:
35/10 = 3.5
Similarly, if we compare side BC (length 14) to side B'C' (length 49), we get:
49/14 = 3.5
And if we compare side AC (length 16) to side A'C' (length 56), we get:
56/16 = 3.5
Since all the side length ratios are equal to 3.5, the scale factor of the single dilation between triangle ABC and triangle A'B'C' is 3.5.