Affine Transformation of a Quadrilateral

An affine transformation of a plane can be defined as a transformation of the plane that is the composition of a number of parallel projections.

Given any two triangles ABC and A'B'C' there is a unique affine transformation that takes ABC to A'B'C'.

This means that for a quadrilateral ABCD, if the images A', B', C' are known, the image D' is determined.

Sorry, this page requires a Java-compatible web browser.

In this sketch, the points A, B, C, D are free to be dragged, as are A', B', C'. The point D' is determined as the image of D' by the unique affine transformation that takes triangle ABC to triangle A'B'C'.

Affine transformations are more general than isometries, but if you move the points so that A'B'C' is the image of ABC by an isometry, such as a line reflection or a translation, then point D' will move so that A'B'C'D' is the image of ABC by the same isometry.

James King, 1/6/2003


This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.