The side lengths of triangle ABC

Question

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

5.6
5.6

27
Start Fraction 2 over 7 End Fraction

3
3

3.5
3.5

Answer 1

To find the scale factor between triangle \( ABC \) and triangle \( A'B'C' \), we can compare the corresponding side lengths of the two triangles.

The side lengths of triangle \( ABC \) are:

• \( 10 \)
• \( 14 \)
• \( 16 \)

The side lengths of triangle \( A'B'C' \) are:

• \( 35 \)
• \( 49 \)
• \( 56 \)

We can calculate the scale factor for each pair of corresponding sides:

1. Scale factor based on \( 10 \) and \( 35 \): \[ \text{Scale Factor} = \frac{35}{10} = 3.5 \]

2. Scale factor based on \( 14 \) and \( 49 \): \[ \text{Scale Factor} = \frac{49}{14} = 3.5 \]

3. Scale factor based on \( 16 \) and \( 56 \): \[ \text{Scale Factor} = \frac{56}{16} = 3.5 \]

All three pairs give the same scale factor of \( 3.5 \).

Therefore, the scale factor of the dilation from triangle \( ABC \) to triangle \( A'B'C' \) is \( \boxed{3.5} \).