What Is Rigid Transformation?

All transformations retain the same shape even if they change size.

Transformations are geometrical shapes that have had their coordinates relocated. They are sometimes flipped over like a mirror reflection or slid over to a new location. Transformations can even change the size of a shape. Rigid transformations are a very particular type of transformation.

Occurrence

A transformation occurs in geometry when a shape is moved to a different position to create a new shape. The original shape, or preimage, can be rotated, reflected or dilated.

Criteria

If a image retains its original dimensions, the new shape or image is called a rigid transformation. If the image is is re-sized, it is said to be dilated. A dilated image changes size but remains proportional to the preimage, like a scale model. A rigid transformation may be rotated or reflected but the actual dimensions the same.

Significance

Geometrical transformations illustrate concepts such as scale and ratio. They also show how to shapes can remain congruent, or identical, even if the shapes change orientation or position.

References

• University of Georgia Department of Mathematics: Introduction to Transformations
• Math Warehouse: Transformations in Math

Resources

• Maths Net: Transformation