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 3 3.5 3.5 27 Start Fraction 2 over 7 End Fraction 5.6 5.6

Answer 1

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

The side lengths of triangle ABC are:

• a = 10
• b = 14
• c = 16

The side lengths of triangle A′B′C′ are:

• a′ = 35
• b′ = 49
• c′ = 56

To find the scale factor, we can divide the lengths of the sides of triangle A′B′C′ by the lengths of the corresponding sides of triangle ABC. Let's calculate it for each pair of corresponding sides:

1. For sides = 10 and 35: \[ \text{Scale Factor} = \frac{35}{10} = 3.5 \]

2. For sides = 14 and 49: \[ \text{Scale Factor} = \frac{49}{14} = 3.5 \]

3. For sides = 16 and 56: \[ \text{Scale Factor} = \frac{56}{16} = 3.5 \]

Since all ratios give the same scale factor, the scale factor of the dilation from triangle ABC to triangle A′B′C′ is \(3.5\).

Thus, the correct response is \( \boxed{3.5} \).