§6 Transformations of Figures
Transformations — also called mappings — are systematic rules that move, reflect, rotate, or scale every point of the plane in a uniform way. By studying them we gain a unified language for describing congruence and similarity: two figures are congruent when one can be mapped onto the other by an isometry, and similar when a similarity transformation connects them.
Learning Objectives
By the end of this chapter you will be able to:
- Define a transformation of the plane as a bijection and distinguish isometries from other mappings
- Perform parallel translations and determine translation vectors from given pairs of corresponding points
- Reflect figures across any line and identify axes of symmetry
- Apply central symmetry and recognise figures that possess a centre of symmetry
- Rotate figures about any centre by a given angle using the rotation formulas
- Carry out homotheties with any centre and ratio, and connect homothety to similarity transformations
- Use the area-ratio rule for similar figures ()