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

Answer 1

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

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 by dividing the corresponding side lengths of triangle A′B′C′ by the side lengths of triangle ABC.

1. For the side of length 10 in triangle ABC: \[ \text{Scale Factor} = \frac{35}{10} = 3.5 \]

2. For the side of length 14 in triangle ABC: \[ \text{Scale Factor} = \frac{49}{14} = 3.5 \]

3. For the side of length 16 in triangle ABC: \[ \text{Scale Factor} = \frac{56}{16} = 3.5 \]

Since the scale factor is consistent across all corresponding sides, we conclude that the scale factor of the dilation is 3.5.