Question

Dilations Quick Check
3 of 53 of 5 Items
Question
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
3

3.5
3.5

Answer 1

To find the scale factor of the dilation between triangle ABC and triangle A′B′C′, you can compare the corresponding side lengths of the two triangles.

The side lengths of triangle ABC are 10, 14, and 16, and the corresponding side lengths of triangle A′B′C′ are 35, 49, and 56.

To find the scale factor \( k \), you can use any pair of corresponding sides.

Using the side 10 from triangle ABC and the side 35 from triangle A′B′C′:

\[
k = \frac{\text{side length of A′B′C′}}{\text{side length of ABC}} = \frac{35}{10} = 3.5
\]

You can check with another pair:

Using the side 14 from triangle ABC and the side 49 from triangle A′B′C′:

\[
k = \frac{49}{14} = 3.5
\]

Using the side 16 from triangle ABC and the side 56 from triangle A′B′C′:

\[
k = \frac{56}{16} = 3.5
\]

In all cases, the scale factor is 3.5.

So, the correct answer is:

**3.5**