Transformation II

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MATHEMATICS FORM 3 CHAPTER 10 TRANSFORMATION II Mathematics Form 3

Transcript of Transformation II

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MATHEMATICS FORM 3

CHAPTER 10

TRANSFORMATION IIMathematics Form 3

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Lesson contents

Identify an enlargement

The scale factor of an enlargement

Determine the image of enlargement

Exercises

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Enlargement is a type of transformation whereby all the points of an object move from a fixed point at a constant ratio.

The centre of enlargement = a fixed point or invariant point

The constant ratio = the scale factor

The image of an enlargement is similar in shape to the original object, but different in size.

The image and object are similar figures.

Transformation II

Identify an enlargement

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Transformation II

• Identify whether the following transformations are enlargements.

Enlargement ExamplesExamples

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Solution

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Transformation II

• Identify whether the following transformations are enlargements.

Enlargement ExamplesExamples

• The transformation is an enlargement.• The two shapes are similar and the corresponding sides are parallel.

Solution 11

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Transformation II

• Identify whether the following transformations are enlargements.

• The transformation is not an enlargement.• The two shapes are not similar and the corresponding sides are not parallel.

Enlargement

Solution

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ExamplesExamples

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object of side ofLength

image side ofLength

tenlargemen of centre object to from Distance

tenlargemen of centre toimage from Distancek factor Scale

QR

R'Q'PR

PR'

PQ

PQ'

k

Under an enlargement, all the points of an object move from a fixed point at a constant ratio. This constant ratio is known as the scale factor.

If Q’R’ is the image of QR under an enlargement with centre P,

The scale factor of an enlargement

Transformation II

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Transformation II

Determine the image of enlargement

Example 2Example 2Example 1Example 1

Scale factor = 2 Scale factor = -1

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Transformation II

Determine the image of enlargement

From O, draw a straight line that passes through one point of the object, such as R.

Step 1Step 1

Step 2Step 2

Step 3Step 3

Step 4Step 4

Example 1Example 1

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Transformation II

Determine the image of enlargement

Use the compasses to mark a point R’ on the straight line so that OR’ = kOR.

Step 1Step 1

Step 2Step 2

Step 3Step 3

Step 4Step 4

Example 1Example 1

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Transformation II

Determine the image of enlargement

Repeat steps 1 and 2 to determine the positions of P’ and Q’.

Step 1Step 1

Step 2Step 2

Step 3Step 3

Step 4Step 4

Example 1Example 1

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Transformation II

Determine the image of enlargement

Join R’, P’ and Q’ to form an image of ▲PQR.

Step 2Step 2

Step 3Step 3

Step 4Step 4

Step 1Step 1

Example 1Example 1

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Transformation II

Determine the image of enlargement

Step 1Step 1

Step 2Step 2

Step 4Step 4

Step 3Step 3

From O, draw a straight line that passes through one point of the object, such as R.

Example 2Example 2

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Transformation II

Determine the image of enlargement

Step 1Step 1

Step 2Step 2

Step 4Step 4

Step 3Step 3

Use the compasses to mark a point R’ on the straight line so that OR’ = kOR.

Example 2Example 2

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Transformation II

Determine the image of enlargement

Step 1Step 1

Step 2Step 2

Step 3Step 3

Step 4Step 4

Repeat steps 1 and 2 to determine the positions of P’ and Q’.

Example 2Example 2

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Transformation II

Determine the image of enlargement

Step 1Step 1

Step 2Step 2

Step 3Step 3

Step 4Step 4 Join R’, P’ and Q’ to form an image of ▲PQR.

Example 2Example 2

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Transformation II

Exercises • Draw the image of the object under an enlargement with centre O and scale factor k.

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k = -1

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Transformation II

Exercises

• Draw the image of the object under an enlargement with centre O and scale factor k.

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k = ½

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Transformation II

Exercises • Draw the image of the object under an enlargement with centre O and scale factor k.

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k = 2

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Transformation II

Worksheet

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the end

Created by ili & saa(2009)