Dilation Rule Calculator

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.