Dilation Rule Calculator
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Dilation is a transformation that resizes an object in a plane. The dilation rule involves enlarging or shrinking points from a center by a scale factor. The formula for dilation of a point \( (x, y) \) with respect to a center \( (cx, cy) \) and a scale factor \( s \) is:
\[ x' = cx + s(x - cx) \] \[ y' = cy + s(y - cy) \]
This calculator helps you find the new coordinates of a point after dilation.
Example Calculation
For a point (3, 4), a center at (1, 1), and a scale factor of 2:
\[ x' = 1 + 2(3 - 1) = 5 \] \[ y' = 1 + 2(4 - 1) = 7 \]
So, the dilated point is (5, 7).
Usage Scenarios
- Geometry: Dilation is widely used in geometric transformations.
- Scaling images: This concept helps with scaling graphics without distortion.