Question

Which statement about the dilation of these triangles is true?

A pre-image triangle has side lengths 4, 5, 3. An image triangle has side lengths 4 (2), 5 (2), 3 (2).
The scale factor is One-half.
The scale factor is 2.
The scale factor is 3.
The scale factor is 4.

Answer 1

To determine the scale factor between the pre-image triangle and the image triangle, we need to compare the corresponding side lengths.

The pre-image triangle has side lengths of 4, 5, and 3.

The image triangle has side lengths of:
- 4 (2) = 4 * 2 = 8
- 5 (2) = 5 * 2 = 10
- 3 (2) = 3 * 2 = 6

So the side lengths of the image triangle are 8, 10, and 6.

Now, we can find the scale factor by comparing the lengths of the corresponding sides:

- For the first side, the ratio is \( \frac{8}{4} = 2 \).
- For the second side, the ratio is \( \frac{10}{5} = 2 \).
- For the third side, the ratio is \( \frac{6}{3} = 2 \).

Since all ratios are equal to 2, the scale factor is 2.

Therefore, the true statement about the dilation of these triangles is:
**The scale factor is 2.**