Centre of enlargement

Centre of enlargement

Centre of enlargement

• OBJECTIVE

• Understand centre of enlargement and scale factors, negative and positive and less than 1

• SUCCESS CRITERIA• Identify centre of enlargement• Identify scale factor• Enlargement greater than 1• Enlargement less than 1• Enlargements that are negative

Key words

• Centre of enlargement• Scale factor• Corresponding• Positive• Negative• Less than• Greater than

• Fraction• Line• Extend• Rotate• Multiply• Coordinates• Vertices • Enlargement

Centre of enlargement• The centre of enlargement gives the position

from which the enlargement will take place• When we blow up a balloon the centre of

enlargement would be from the spout where the gas was entering

• If we shine a light at an object so that its shadow appeared on a wall. The shadow would be an enlargement of the original figure and the light source would be the centre of enlargement.

Centre of enlargement

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1 3 5 7 9 11 13 15 17 19Centre of enlargement (3, 3)

Corresponding vertices

Centre of enlargement – positive scale factor greater than 1

• When the scale factor is positive then the enlargement appears on the same side of the centre of enlargement as the original shape.

• The drawing will show centre of enlargement, original shape and enlarged shape in that order.

Centre of enlargement – positive scale factor greater than 1

• Draw lines from the centre of enlargement through the vertices of the original shape

• The length from the centre of enlargement to the original shape is increased by the scale factor to determine the vertices of the enlarged shape

• The position of the new shape is always measured from the centre of enlargement

Centre of enlargement – positive scale factor

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This shows shape A enlarged by a scale factor of 2 about the centre of enlargement (4, 3)

The length of the line from the centre of enlargement to the original shape is increased by the scale factor

Centre of enlargement – positive scale factor

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Enlarge this shape by a scale factor of 3 about the centre of enlargement (3, 3)

Centre of enlargement – positive scale factor

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The lines from the centre of enlargement to the original shape are increased by a scale factor of 3 to provide the position of the enlarged shape

Centre of enlargement – exercise 1enlarge both shapes by a scale factor of 3 about the centres of enlargement indicated

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Centre of enlargement – exercise 1answer

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Enlarge both shapes by a scale factor of 2 about the centres of enlargement indicated

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Enlarge both shapes by a scale factor of 2 about the centres of enlargement indicated

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Enlarge both shapes by a scale factor of 3 about the centres of enlargement indicated

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Enlarge both shapes by a scale factor of 3 about the centres of enlargement indicated

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Centre of enlargement – negative scale factor

• When the scale factor is negative then the enlargement appears on the opposite side of the centre of enlargement as the original shape.

• The drawing will show original shape, centre of enlargement and enlarged shape in that order.

Centre of enlargement – negative scale factor

• Draw lines from the vertices of the original shape through the centre of enlargement

• The length from the centre of enlargement to the original shape is increased by the scale factor to determine the vertices of the enlarged shape

• The position of the new shape is always measured from the centre of enlargement

Centre of enlargement – negative scale factor

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This shows shape A enlarged by a scale factor of -2 about the centre of enlargement (10, 7)

Centre of enlargement – negative scale factor

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Enlarge this shape by a scale factor of -3 about the centre of enlargement (3, 3)

Centre of enlargement – negative scale factor

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Enlarge this shape by a scale factor of -3 about the centre of enlargement (3, 3)

The length of the line from the C of E to the enlargement is 3 times the length of the line from the shape to the C of E

Centre of enlargement – scale factor of -1An enlargement by a scale factor of -1 is the same as a

rotation of 1800 about the same point

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This shows shape A enlarged by a scale factor of -1 about the centre of enlargement (10, 7)

This is the same as a rotation of 1800 about centre of rotation (10, 7)

Centre of enlargement – exercise 2enlarge both shapes by a scale factor of -2 about the centres of enlargement indicated

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Centre of enlargement – exercise 2answer

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Enlarge each shape by a scale factor of -3

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Enlarge each shape by a scale factor of -3

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Centre of enlargement – Positive scale factor less than 1

• When the scale factor is less than 1 then the enlargement appears between the centre of enlargement and the original shape.

• The drawing will show original shape, enlarged shape and centre of enlargement in that order.

• We still call it an enlargement although it is smaller.

Centre of enlargement – Positive scale factor less than 1

• Draw lines from the vertices of the original shape to the centre of enlargement.

• The length from the centre of enlargement to the original shape is multiplied by the scale factor to determine the vertices of the enlarged shape.

• The position of the new shape is always measured from the centre of enlargement.

Centre of enlargement – scale factor less than 1

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This shows shape A enlarged by a scale factor of ½ about the centre of enlargement (4, 3)

Centre of enlargement – scale factor less than 1

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Enlarge the shape by a scale factor of 1/3 about the centre of enlargement (3, 3)

Centre of enlargement – scale factor less than 1

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Enlarge the shape by a scale factor of 1/3 about the centre of enlargement (3, 3)

Centre of enlargement – scale factor less than 1enlarge both shapes by a scale factor of 1/3 about the Centre

of Enlargements indicated

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Centre of enlargement – scale factor less than 1enlarge both shapes by a scale factor of 1/3 about the Centre

of Enlargements indicated

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Finding the Centre of enlargement

• To find the centre of enlargement we must draw lines through the corresponding vertices of both shapes.

• Where the lines cross is the centre of enlargement

Find Centre of enlargement

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This shows that the centre of enlargement is (1, 1)This is found by drawing lines through the corresponding vertices of the shapes.

Finding the Centre of enlargement

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Find the centre of enlargement.

Finding the Centre of enlargement

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Find the centre of enlargement.

Find the centre of enlargement - exercise

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Find the centre of enlargement – answer(2, 2) and (19, 1)

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Finding the scale factor

• To find the scale factor we divide a length on the enlarged shape by a corresponding length on the original shape

• Scale factor = enlarged length ÷ original length

Find the scale factor of enlargement

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The scale factor from the smaller shape to the larger shape is 3This is found by comparing the lengths of the corresponding sides.

2 × scale factor = 6Scale factor = 6 ÷ 2 = 3

Find the scale factor of enlargement for these shapes - exercise

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Find the scale factor of enlargement for these shapes answer 2 and 3

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Centre of enlargementEnlarge shape A about (1, 2) by a scale factor of

a) 3 b) -4 c) -1

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-10 -8 -6 -4 -2 2 4 6 8 10

-2

-4

-6

Centre of enlargementenlarge shape A about (1, 2) by a scale factor of

a) 3 b) -4 c) -1

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-10 -8 -6 -4 -2 2 4 6 8 10

-2

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a) 2

c) -1

b) -4

Centre of enlargement - review

• Identify centre of enlargement• Identify scale factor• Enlargement greater than 1• Enlargement less than 1• Enlargements that are negative

Complete the paragraph using the words below

The centre of enlargement is a point from which a shape is enlarged. Positive scale factors --------- --------- one produce shapes that are larger than the original shape so that the centre of enlargement, original shape and --------- shape appear in that order. Negative

--------- --------- less than minus one produce enlarged shapes that appear rotated. Scale factors less than one produce smaller enlargements although we still call them enlargements. To find the --------- -- --------- we draw lines through the corresponding --------- of the shapes. The coordinates where these --------- meet is the centre of enlargement.

Centre of enlargement, Scale factors, Corresponding, Positive, Negative, Less than, Greater than, Fraction, Lines, Extend, Rotate, Multiply, Coordinates, Vertices, Enlarged

Complete the paragraph using the words below

The centre of enlargement is a point from which a shape is enlarged. Positive scale factors greater than one produce shapes that are larger than the original shape so that the centre of enlargement, original shape and enlarged shape appear in that order. Negative scale factors less than minus one produce enlarged shapes that appear rotated. Scale factors less than one produce smaller enlargements although we still call them enlargements. To find the centre of enlargement we draw lines through the corresponding vertices of the shapes. The coordinates where these lines meet is the centre of enlargement. Centre of enlargement, Scale factors, Corresponding, Positive, Negative, Less than, Greater than, Fraction, Lines, Extend, Rotate, Multiply, Coordinates, Vertices, Enlarged