It seems like you've referenced a geometric transformation involving dilation, but I don't have specific details about the figure you want to dilate, the center of dilation, or the scale factor.
To help you with the dilation process, here's how you can do it step by step:
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Identify the Original Points: List the coordinates of the points of the shape you want to dilate. For example, if you have a triangle with vertices A(1, 2), B(3, 4), and C(5, 6).
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Determine the Center of Dilation: Let’s assume the center of dilation is point O (x_o, y_o). For example, let’s say O(2, 2).
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Choose a Scale Factor: Specify a scale factor k. For example, k = 2 means you want to make the shape twice as large.
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Apply the Dilation Formula: Use the formula for dilation: \[ (x', y') = (x_o + k(x - x_o), y_o + k(y - y_o)) \] where (x', y') are the coordinates of the transformed point after dilation.
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Calculate New Points: For each point in the original shape, apply the dilation formula to find the new coordinates.
Let’s say you have one of the points:
- For point A(1, 2): \[ (x', y') = (2 + 2(1 - 2), 2 + 2(2 - 2)) = (2 - 2, 2 + 0) = (0, 2) \]
- Repeat this for each point.
- Plot the New Points: Once you have all the new points, plot them on a graph.
If you provide specific coordinates, center of dilation, and scale factor, I can assist you by calculating the precise new coordinates of your shape.