Key Concepts: Dilations

Definition

A dilation is a transformation that changes the size of a figure by a scale factor k relative to a center point.

Coordinate Rule (center at origin)

(x, y) → (kx, ky)

Scale Factor

• If |k| > 1: the image is an enlargement.
• If 0 < |k| < 1: the image is a reduction.
• If k < 0: the image is on the opposite side of the center.

Properties

• A dilation is not an isometry (it does not preserve distances unless k = ±1).
• Dilations preserve angle measures and shape (they produce similar figures).
• The ratio of image to pre-image lengths is |k|.