## A: Translations

A **translation** is descrbed using a vector

( | a |
) |

b |

This moves a point** a** horizontally and **b **vertically.

Exercise 20A pg 404

## B: Rotations

A rotation is defined by a **direction**, **angle** and **centre** of rotation.

Ex 20B Pg 406

## C: Reflections

Only the **Line of Reflection** is needed to define the transformation.

Ex 20C pg 407

## Transformation Geometry

*The following series of links have been put together collate to facilitate the home study of Chapter 20 - Transformation Geometry during the Autumn break.*

**Outline**

The first three transformation to be examined only moves the shape. The transformation creates a** ****congruent shapes**

A: Translations

B: Rotations

C: Reflections

Enlargements and reductions create **similar shapes** D: Enlargements and Reductions

Stretches distort the shape

E: Stretches

Applications of Transformations to functions

F: Transforming Functions

G: The Inverse of a Transformation

H: Combinations of Transformation

## D: Enlargements and Reductions

An enlargement or reduction is defined by a **centre** and **scale factor (SF).** If

** **SF > 1 enlargement

0 < SF < 1 reduction

SF < 0 ends on the other side of the centre

Ex 20D pg 409

## G: The Inverse of a Transformation

If a transformation maps and object to an image then the** inverse transformation** maps the image back to the object.

Ex 20G pg 417

## H: Combinations of Transformations

The transformation of an object by the combination of transformation G followed by transformation H is expressed as HG.

We are often asked to represent this as a single transformation.

Ex 20H pg 418

## E: Stretches

Stretches are defined by a **stretch factor **and** invariant line**

**Invariant x-axis **scale

*factor*

*k*

* (x, y) → (x, ky)*

**Invariant y -axis **scale

*factor*

*k*

* (x, y) → (kx, y)*

Ex 20E pg 412

## F: Transformations of Functions

A **translation vector**

( | h |
) |

k |

applied to a function maps **y = f(x)** onto

**y = f(x - h) + ***k*

** **

A** stretch **with x as the invarient axis and scale factor k applied to a function maps **y = f(x)** onto **y = kf(x)**

Ex 20F pg 415