# transformation ii

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Mathematics Form 3

TRANSFORMATION IIM AT H E M AT I C S F O R M 3 CHAPTER 10

Lesson contentsIdentify an enlargement The scale factor of an enlargement Determine the image of enlargement Exercises

Transformation II

Identify an enlargement

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

Enlargement

Examples Identify whether the following transformations are enlargements.

Solution

12

Transformation II

Enlargement

Examples Identify whether the following transformations are enlargements.

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

12

Transformation II

Enlargement

Examples Identify whether the following transformations are enlargements.

Solution

12

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

Transformation II

The scale factor of an enlargement

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.

Scale factor k

Distance from image to centreof enlargement Distance from object to centreof enlargement Length of side image Length of side of object

If QR is the image of QR under an enlargement with centre P, PQ' k PQ PR' PR Q' R' QR

Transformation II

Determine the image of enlargement

Example 1

Example 2

Scale factor = 2

Scale factor = -1

Transformation II

Determine the image of enlargement

Example 1

Step 1 Step 2 Step 3 Step 4

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

Transformation II

Determine the image of enlargement

Example 1

Step 1 Step 2 Step 3 Step 4

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

Transformation II

Determine the image of enlargement

Example 1

Step 1 Step 2 Step 3 Step 4 Repeat steps 1 and 2 to determine the positions of P and Q.

Transformation II

Determine the image of enlargement

Example 1

Step 1 Step 2 Step 3 Step 4 Join R, P and Q to form an image of PQR.

Transformation II

Determine the image of enlargement

Example 2

Step 1 Step 2 Step 3 Step 4

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

Transformation II

Determine the image of enlargement

Example 2

Step 1 Step 2 Step 3 Step 4

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

Transformation II

Determine the image of enlargement

Example 2

Step 1 Step 2 Step 3 Step 4 Repeat steps 1 and 2 to determine the positions of P and Q.

Transformation II

Determine the image of enlargement

Example 2

Step 1 Step 2 Step 3 Step 4 Join R, P and Q to form an image of PQR.

Transformation II

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

12 3

k = -1

Transformation II

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

1

23

k=

Transformation II

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

1 2

3

k=2

Transformation II

Worksheet