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Mathematics - Ms. Heather and Mr. DeJong  

Last Updated: Oct 13, 2015 URL: http://metropolitanschool.libguides.com/maths_heather Print Guide
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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

     

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