To determine the magnitude of the dilation from parallelogram ABCD to parallelogram A'B'C'D', we need to analyze the coordinates of points A, B, C, D and A', B', C', D'.
The dilation formula is:
\[ \text{Dilation factor} = \frac{\text{Distance from origin to A'}}{\text{Distance from origin to A}} \]
If we had the coordinates or distances from the origin for both sets of points, we could calculate the dilation factor directly.
Since the specific coordinates are not provided, we can analyze the provided answer choices.
If we assume that the larger parallelogram is being scaled down to the smaller one, typical dilation factors are either fractions less than 1 (indicating a contraction) or whole numbers greater than 1 (indicating an expansion).
Given the options, we can suspect that the dilation factor is likely less than 1, as we are moving from larger to smaller:
- \( \frac{1}{2} \)
- \( \frac{1}{3} \)
These two fractions indicate a reduction (dilation) of size. Without specific coordinates, we can't definitively calculate the dilation, but if we were to choose one of these based on common dilation patterns for similar problems, we might reasonably conclude that the dilation might be either \( \frac{1}{2} \) or \( \frac{1}{3} \).
If the image were provided, we could find the distances and confirm the best answer, but with standard practice, you would need specific lengths. For now, it seems reasonable to lean towards either \( \frac{1}{2} \) or \( \frac{1}{3} \).
Given the limited options and knowledge of typical dilations for geometric figures, I would select:
Start Fraction 1 over 2 End Fraction (1/2)
as a common ratio in dilation scenarios unless indicated otherwise.
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