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Transforming

Space

A S 12.3.6

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Translation- moving the object a fixed

distance along a line.

Reflection- moving (folding) the objectacross a line (axis).

Rotation- moving the object around a point.

Transforming an object meanschanging its position or appearance

e.g.

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When an object is dilated (enlarged orreduced), the image is mathematicallysimilar to the object, but a different sizethan the original.

To describe a dilation you need a centre ofdilation and a scale factor e.g.

DilationsDilations

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All lengths in all dimensions aremultiplied by the same amount,producing an image that has the sameproportions as the original.

http://www.nhb.gov.sg/ACM/acm.shtml

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object

Centre: Tells us from where the

dilation is measure.

Hint: Join centre X with the vertices of thetriangle in a straight line.

Mark points on the lines according to scale

Lets sketchLets sketch

Reduction of 2 :XA /

XA

= XB /XB

= 1/2

etc.

X

A

A

AB

B

B

Enlargement of 1,5 :XA /XA =

XB /XB =3/2 etc.

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If the triangle is in a Cartesian plane,we can use the co-ordinates.

e.g. enlarge ABC with a scale factor1/2 ,

centred about the origin (0;0).

0 1 2 3 4 5

5

4

3

2

1

0

Object:

A(4;4),B(2;2),C(4;2)

Image:A(2;2),B(1;1),C(2;1)

A

B CWhat are the co-

ordinates of theimage?

A

BC

mapping:

(x, y) ( x, y)

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Enlarge ABC by a factor of 3 relativeto the origin with A(2,3), B(3,1),C(1,1).

mapping: (x, y) (3x, 3y)

dilatation centre

= origin O

A

C B

Image A'B'C'is

A'(6, 9), B'(6,3), C'(3, 3)

A

BCo

Lets tryLets try

1.

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A B

CD

If the centre is not outside the object.

Enlarge the shape witha scale factor ,centre A

Enlarge the shapewith a scale factor 2,centre O.

O

A

A

D AD= AD etc.

B

OA = 2 OA etc.

2.

3.

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ConclusionConclusion

If you rotate, reflect and/or translate an

objectthen the image is congruent to the object.Shape & size (sides and angles) do not

change.

If one object becomes another using

transformation, then the two objectsare either congruent or similar.

If you resize or dilate an object then the

image is similar and in proportion to the

object. Shape & angles remain thesame.

Transformational geometry is used in art,textiles, architecture, cultural designs and innature.

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The Mola-Mola Lion Park commissions agiant statue of a lion based on thesketch below. The statue must be 2,5mhigh.

Find the scale factor of the statue.

5cm

Task

Write a report detailing the size of at least 3

parts of the statue, such as diameter of theeye, width of head etc. The mass of thestatue must also be the same as that of theaverage male lion. Research this mass. Useit to calculate the cost of the statue at R425per kg. Add it to your report.

Your company bids to

make the statue.

2500 /5 = 50:1

Your Task