To determine the magnitude of dilation, you need to analyze the coordinates of the original polygon ABCD and the dilated polygon A′B′C′D′. The dilation from the origin involves multiplying the coordinates of each vertex of polygon ABCD by the same dilation factor (k) to obtain the coordinates of polygon A′B′C′D′.
The formula for dilation with respect to the origin is:
\[ (x, y) \rightarrow (kx, ky) \]
Where:
- \( (x, y) \) are the coordinates of the original figure,
- \( (kx, ky) \) are the coordinates of the dilated figure,
- \( k \) is the dilation factor.
You typically identify a point from both polygons, compare the original and dilated coordinates, and use the formula to find \( k \). For instance, if a point from ABCD has coordinates (2, 3) and the corresponding dilated point A′B′C′D′ has coordinates (4, 6), you would set up the equation as follows:
- From (2, 3) to (4, 6):
- \( k \cdot 2 = 4 \) → \( k = 2 \)
- \( k \cdot 3 = 6 \) → \( k = 2 \)
Once the dilation factor \( k \) is determined, that is the magnitude of dilation.
If you are not provided with the specific coordinates in your question, you would need to refer to the image you mentioned for the coordinates of points A, B, C, and D, and perform similar calculations.
Given the multiple-choice options you listed, if you can analyze your image and determine the dilation factor, you would select the correct answer accordingly.
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