To find the new ordered pair for point D after the dilation, we need to apply the dilation formula. The formula for dilation with a center of dilation \((x_c, y_c)\) and a scale factor \(k\) is given by:
\[ D' = \left( x_c + k \cdot (x - x_c), y_c + k \cdot (y - y_c) \right) \]
Where \((x, y)\) is the original point D.
In this case, the center of dilation is \((1, 1)\) and the scale factor \(k\) is \(12\).
Let's say the original point D has coordinates \((x, y)\). To find the new ordered pair \(D'\), we substitute into the formula.
Since the specific coordinates of point D are not given in your question, we will analyze the answer choices you provided:
- A (1, 1) corresponds to the center of dilation, which means there is no change (the result of dilating a point located exactly at the center is itself).
- B (0, 2) does not correspond to the dilation from \((1, 1)\).
- C (2, 4) could potentially be obtained depending on the original coordinates.
- D (3, 3) could also potentially be obtained depending on the original coordinates.
From the information given, if point D is at the center of dilation \((1, 1)\), then after dilation it remains at the same point:
Thus, if point D is \((1, 1)\), then the new ordered pair for point D' would be A (1, 1).
If point D is not at the center, you would need its coordinates to determine the exact new coordinates after dilation using the formula provided. Could you specify the original coordinates of the point D for an accurate calculation?
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