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MATHEMATICS FORM 3
CHAPTER 10
TRANSFORMATION IIMathematics Form 3
Lesson contents
Identify an enlargement
The scale factor of an enlargement
Determine the image of enlargement
Exercises
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
Transformation II
• Identify whether the following transformations are enlargements.
Enlargement ExamplesExamples
11
22
Solution
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
22
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
22
11
ExamplesExamples
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
Transformation II
Determine the image of enlargement
Example 2Example 2Example 1Example 1
Scale factor = 2 Scale factor = -1
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
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
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
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
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
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
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
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
Transformation II
Exercises • Draw the image of the object under an enlargement with centre O and scale factor k.
33
11
22
k = -1
Transformation II
Exercises
• Draw the image of the object under an enlargement with centre O and scale factor k.
33
11
22
k = ½
Transformation II
Exercises • Draw the image of the object under an enlargement with centre O and scale factor k.
11
22
k = 2
33
Transformation II
Worksheet
Click here
the end
Created by ili & saa(2009)