© T Madas

© T Madas

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement

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Centre of Enlargement

© T Madas

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement

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Can you see where the rest of the shape will be?

© T Madas

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement

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Can you see where the rest of the shape will be?

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© T Madas

Enlarge this rectangle by a scale factor of 2 about the marked centre of enlargement

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Can you see where the rest of the shape will be?

© T Madas

Why is the centre of enlargement important?

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© T Madas

Why is the centre of enlargement important?

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© T Madas

Why is the centre of enlargement important?

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© T Madas

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Why is the centre of enlargement important?

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© T Madas

Why is the centre of enlargement important?

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To enlarge a shape you need:

A Scale Factor

Centre of Enlargement

(Size)

(Position)

© T Madas

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement

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Can you see where the rest of the shape will be?

© T Madas

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement

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© T Madas

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement

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© T Madas

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement

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© T Madas

Enlarge this shape by a scale factor of 3 about the marked centre of enlargement

C OI

© T Madas

The Different Positionsof the

Centre of Enlargement

© T Madas

The centre of enlargement can lie on a corner of the shape

C

x 4

x 3

x 2

© T Madas

C

The centre of enlargement can lie on a side of the shape

x 2x 3

© T Madas

C

The centre of enlargement can lie inside the shape

x 2x 3

© T Madas

Formal Enlargementon square paper

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If you are using square paper you can use the following method to enlarge:

C

Scale factor 3

© T Madas

If you are using square paper you can use the following method to enlarge:

24

x 36

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C

Scale factor 3

© T Madas

Finding TheCentre of Enlargement

© T Madas

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Where is the centre of enlargement?

C

© T Madas

Where is the centre of enlargement?

CO

I

© T Madas

Scale Factor Pairs

© T Madas

C BA

x 2What is the scale factor from A to B?

x ½What is the scale factor from B to A?

© T Madas

C

B

A

What is the scale factor from A to B?

What is the scale factor from B to A?x 1

3

x 3

© T Madas

What is the scale factor from A to B?

What is the scale factor from B to A?x 2

3

BAC

x 32

The scale factors which transform object to image and vice versa are always reciprocals of each other

© T Madas

NegativeScale

Factors

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What is the meaning of a negative scale factor?

© T Madas

AB

C

+ve-ve

Enlarge object A by a scale factor of -1

What is the scale factor from B to A?

What other single transformation would have produced the same result from A to B?

© T Madas

AB

C

Enlarge object A by a scale factor of -1

The Enlargement with scale factor -1 and a given centre of enlargement C is the same as a rotation by 180° about C , and C is also known as centre of symmetry

© T Madas

AB

C

Enlarge object A by a scale factor of -1

-2

© T Madas

AC

Enlarge object A by a scale factor of -1

-2

B

What is the scale factor from B to A?

What combination of transformations would have produced the same result from A to B?

– 12

© T Madas

© T Madas

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Enlarge the triangle shown below by a scale factor of 3, with centre of enlargement the origin.

© T Madas

© T Madas

Enlarge the triangle shown below by a scale factor of 2½, with centre of enlargement the point P.

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© T Madas

© T Madas

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Enlarge the trapezium shown below by a scale factor of ½, with centre of enlargement the origin.

© T Madas

© T Madas

4. Enlarge shape P by a scale factor of ½ about (3,14) to give shape R.

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Shape P is enlarged to give shape Q.One side of shape Q is drawn for you.

1. What is the scale factor for this enlargement?2. Complete shape Q. 3. What are the co ordinates of the centre of enlargement?

P

Qthe scale factor from P to Q is2

the centre of enlargement is at (0,0)

R

© T Madas

Exam Question-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

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© T Madas

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

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Enlarge this triangle by a scale factor of 1½, about P

P

© T Madas

© T Madas

Shape P is enlarged to give shape Q.

One of the sides of shape Q has been drawn on the grid.

1. State the scale factor for this enlargement.

2. Complete shape Q on the grid.

QP

The scale factor is½

A AB

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B

CD

E

© T Madas