Question

figure a is dilated to form figure d. what is the scale factor of the dilation? scale factor =

Explanation:

Step1: Determine the length of corresponding sides

Let's assume the side length of figure \(A\) is \(1\) unit (for simplicity, by counting the grid - squares for a small segment). For figure \(D\), the corresponding side length (by counting the grid - squares for the larger, corresponding segment) is \(3\) units.

Step2: Calculate the scale factor

The formula for the scale factor \(k\) of a dilation is \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
If the length of the side in the pre - image (figure \(A\)) is \(x = 1\) and the length of the side in the image (figure \(D\)) is \(y=3\), then \(k=\frac{y}{x}\).
Substituting the values, we get \(k = 3\).

Answer:

\(3\)