Question

The distance from O to A is 3 and the distance from A to A prime is 3.
The diagram shows a dilation.

Which dilation does it represent?


What is the scale factor?


Answers

Answered by GPT-4o mini
To determine the dilation represented in your scenario, we need to understand a couple of key points:

1. **Dilation**: Dilation is a transformation that alters the size of a figure but maintains its shape. Dilation is defined by a center point (in your case, point O) and a scale factor.

2. **Scale Factor**: The scale factor is the ratio of the distance from the center of dilation to a point on the original figure compared to the distance from the center of dilation to the corresponding point on the dilated figure.

In your case:

- The distance from O to A is 3.
- The distance from A to A' is also 3.

To find the scale factor (k):

\[
k = \frac{\text{Distance from O to A'}}{\text{Distance from O to A}}
\]

Here, the distance from O to A' is the distance from O to A (3) plus the distance from A to A' (3):

- Distance from O to A' = Distance from O to A + Distance from A to A' = 3 + 3 = 6.

Now substituting this into the formula for scale factor:

\[
k = \frac{6}{3} = 2
\]

So the dilation represents a scale factor of 2.

**Summary**:
- The dilation represents a transformation with a center at O.
- The scale factor is **2**.
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