The image shows a graph with a pair of triangles marked on it. The red triangle is smaller and the green triangle is larger. They are related by a dilation, and the problem is asking to find the scale factor of the dilation.

To determine the scale factor, we need to compare the lengths of corresponding sides of the triangles. Based on the image, it seems like points Q, R, and S from the red triangle are being dilated to corresponding points Q', R', and S' on the green triangle.

Steps to find the scale factor:

1. Identify a pair of corresponding points and their coordinates on the smaller triangle and the larger triangle.
2. Use the formula for scale factor:

$\text{Scale factor} = \frac{\text{Length of side on the larger triangle}}{\text{Length of corresponding side on the smaller triangle}}$

Looking at the image:

• For the red triangle, the base $QR$ goes from $(-2, 0)$ to $(2, 0)$, so the length is 4 units.
• For the green triangle, the base $Q'R'$ goes from $(-10, 0)$ to $(10, 0)$, so the length is 20 units.

Now, we can compute the scale factor:

$\text{Scale factor} = \frac{20}{4} = 5$

Thus, the scale factor of the dilation is 5.

Would you like a detailed breakdown of these steps or have any other questions?

Related Questions:

1. How does changing the center of dilation affect the scale factor?
2. What would the scale factor be if the image were reduced instead of enlarged?
3. Can a dilation have a negative scale factor, and what would that mean geometrically?
4. How can you find the scale factor if you're given the area of both triangles?
5. What happens to the angle measures of a figure after dilation?

Tip:

When working with dilations, always ensure that you are comparing corresponding sides and that you measure distances carefully to avoid errors in finding the scale factor.