TRANSFORMATION

TRANSLATION

ENLARGEMENT

ROTATION

REFLECTION

TRANSLATION

A translation is a movement in a straight line.

In mathematics translations are usually used through co ordinates. They are usually written out as column vectors; for e.g.

2

-2

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( )When doing a translation, the object and the image are congruent

+

+ -

-THINGS TO REMEMBERALWAYS THE FIRST # IN THE COORDINANTS IS FOR GOING HORIZNTALLY AND THE SECOND # IS GOING VERTICALLY!

PREVIOUS INVERSE

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“The inverse” would basically mean the opposite or moving backwards. So the Inverse would

be……

2

-2( ) ( )-2

2

For Example

ENLARGEMENT

The ENLARGEMENT is change in size of a shape.

Unlike a translation, when doing an enlargement the object and the image are not congruent.

A

BC

A

BC

Scale Factor:

2

K

REMEMBER!

When Describing an enlargement, you must mention these two things:

SCALE FACTOR

CENTRE OF ENLARGEMENT

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INVERSE

NEGATIVE ENLARGEMENT

INVERSE

For the inverse of an “Enlargement,” You have to find the reciprocal of the scale factor.

For Example..

Scale Factor:

RECIPROCAL

1 (HALF)

2

INVERSE=

2

AS AN IMAGE CENTRE OF

ENLARGEMENT

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ENLARGEMENT

NEGATIVE ENLARGEMENT

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INVERSE

ENLARGEMENT

NEGATIVE ENLARGEMENT

When dealing with a negative scale factor of an enlargement, the image would appear on the opposite side of the centre of enlargement.

1 2 3 6

123

4

x

y

-1-2-3

-4

P4 5-1-2-3 -4 -5 -6 -7 -8 -9 -10 -11 -12

Enlargement with scale factor =-2 and centre of origin

Co-ordinates of the image=-2 X

the co-ordinates of the object.

(3,1) ---- (-6,-2)

(4,2) ---- (-8,-4)

(5,2) ---- (-10,-4)

(6,1) ---- (-12,-2)

(4,-1)---- (-8, 2)

ROTATION

A rotation is when the image is turns from a fixed point, which is known as the centre of rotation

0 1 2 3 4 5 6 7 8 9 10

123

45678910

11

In the diagram shown, P is mapped onto Q by a rotation of 90 degrees clockwise, centre R (3,2)

P

QR

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INVERSE

0 1 2 3 4 5 6 7 8 9 10

123

45678910

11

P

QR

INVERSE

When dealing with an inverse of a rotation, both the angle and the centre of rotation remain the same; just the turn would be in the opposite direction.

The inverse of the previous diagram would be:

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REFLECTION

A reflection is when every point of an object moves to the same distance on the opposite side of a fixed line.

A B

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INVERSE

INVERSE

The inverse of a reflection would just be reflecting back from where it started.

A B

COMBINATION TRANSFORMATION

A combination transformation is when a number of transformation are combined together.