Dilation Transformation Calculator

Understanding Dilation

In geometry, a dilation is a transformation that changes the size of a figure (either enlarging or shrinking it) but does not change its shape. It is defined by a fixed center point C(c_x, c_y) and a scale factor k.

Each point P(x, y) in the original shape is mapped to a dilated point P'(x', y') along a straight ray originating from C:

P' = C + k(P - C)

Scaling Factors & Effects

k > 1: Enlargement. The shape grows larger and moves further from the center point.
0 < k < 1: Reduction. The shape shrinks and moves closer to the center point.
k = 1: Identity. The points remain in their original positions.
k < 0: Dilation plus reflection. The shape is scaled and flipped across the center point to the opposite side.