Question: ΔA'B'C' is the image of ΔABC under a dilation.
The graph shows two similar triangles: triangle A'B'C' on the left is a larger pink triangle, and triangle ABC on the right is a smaller blue triangle. position_hint: center
What is the scale factor of the dilation?
1. **State the problem:** We are given two similar triangles, ΔA'B'C' (larger) and ΔABC (smaller), where ΔA'B'C' is the image of ΔABC under a dilation. We need to find the scale factor of this dilation.
2. **Recall the formula for scale factor:** The scale factor $k$ of a dilation is the ratio of any corresponding side length in the image to the corresponding side length in the pre-image:
$$k = \frac{\text{length of side in } \Delta A'B'C'}{\text{length of corresponding side in } \Delta ABC}$$
3. **Identify corresponding sides:** From the graph, identify a pair of corresponding sides between the two triangles. For example, if side $A'B'$ corresponds to side $AB$, measure or note their lengths.
4. **Calculate the scale factor:** Suppose $A'B' = 8$ units and $AB = 4$ units (example values from the graph). Then:
$$k = \frac{8}{4} = 2$$
This means the dilation scale factor is $2$, indicating the image triangle is twice as large as the original.
5. **Interpretation:** A scale factor greater than $1$ means the image is an enlargement; a scale factor between $0$ and $1$ means a reduction.
**Final answer:** The scale factor of the dilation is the ratio of corresponding side lengths, for example, $k = 2$ if $A'B' = 8$ and $AB = 4$.
*Note: Replace the example side lengths with actual measurements from the graph to find the exact scale factor.*