Dilation Transformation Calculator

Visualize and calculate the dilation transformation of a point in a coordinate plane.

Input Parameters

Result

Dilated Point Coordinates:

Visualization

Understanding Dilation Transformation

In geometry, dilation is a transformation that enlarges or shrinks an object. It is defined by a center point and a scale factor. The center of dilation is the fixed point around which the object is scaled, and the scale factor determines how much the object is enlarged or shrunk.

If the scale factor is greater than 1, the object is enlarged. If the scale factor is between 0 and 1, the object is shrunk. A scale factor of 1 results in no change, and a negative scale factor results in a dilation followed by a reflection through the center point.

For a point (x, y), a center of dilation (cx, cy), and a scale factor k, the dilated point (x', y') is calculated as:

x' = cx + k * (x - cx) + y' = cy + k * (y - cy)

Use this calculator to easily find the dilated coordinates and visualize the transformation on the graph.