Question

Figure D’E’F’ is a dilation with center (0,0) of figure DEF. What is the scale factor?

(10 Points)


3

6

1/3

1/6

Answer 1

To determine the scale factor of the dilation from figure DEF to figure D'E'F', we need to compare the corresponding lengths of one of the sides of the original figure DEF with the corresponding side of the dilated figure D'E'F'.

Let's denote the lengths of a corresponding side of DEF as L_DEF and the length of the corresponding side of D'E'F' as L_D'E'F'.

The scale factor \( k \) can be found using the formula:

\[
k = \frac{L_{D'E'F'}}{L_{DEF}}
\]

However, since specific measurements of the sides are not provided in your question, let's analyze the answer choices you provided.

If we're given choices of 3, 6, 1/3, and 1/6, we can consider that:

- If the scale factor is greater than 1 (like 3 or 6), D'E'F' would be larger than DEF.
- If the scale factor is between 0 and 1 (like 1/3 or 1/6), D'E'F' would be smaller than DEF.

To determine the correct scale factor, we would typically look for specific lengths of the corresponding sides. Since the does not define any specific dimensions of DEF and D'E'F', I cannot provide a definitive answer without extra information.

However, if you have measurements for the lengths of the sides, simply apply them to compute \( k \) and choose the correct option from your provided choices.

Without additional details, please review the figures or measurements you have to deduce the scale factor.