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2. Enlargements If a shape (object) is enlarged in such a way, that all lengths become twice the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x2. A B Object x2 3 2 A’ Image 6 4 4 3 B’ Image 8 6 We say that the rectangle A has been enlarged by a scale factor of x2 to become image A’. Similarly B’ is the image of triangle B after a x2 enlargement.

3. Enlargements In a similar manner, if a shape (object) is enlarged in such a way, that all lengths become three times the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x3. Object x3 A’ Image A 2 5 4 6 15 12

4. Enlargements Question 1. Object A is to be enlarged by a scale factor of enlargement of x2 and object B by a scale factor of enlargement of x 3. Draw and label the images. The points are there to help you with the positioning of the images. B Object A B’ Image A’ Image

5. Enlargements Question 2. Only one of the triangles shown is an enlargement of triangle A. Which triangle is it and what is the scale factor of enlargement? A B C D E Triangle D, scale factor of enlargement is x 2

6. Enlargements Question 3. Two of the trapezia shown are enlargements of trapezium A. Which trapezia are they and what are the scale factors of enlargement? E is an enlargement by scale factor x2 and C is an enlargement by scale factor x 3 A B D C E F

7. Fractional Enlargements Fractional Scale Factors If a shape (object) is enlarged in such a way, that all lengths become ½ the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR of x½. B’ Image A’ Image x½ A Object B 3 2 6 4 4 3 8 6 x½

8. Enlargements In a similar manner, if a shape (object) is enlarged in such a way, that all lengths become 1/3 the size they were on the original then we say that the shape has been enlarged by a SCALE FACTOR x1/3. x1/3 A Object Image A’ 2 5 4 6 15 12

9. Enlargements Question 4. (a) Enlarge the rectangle by a scale factor of enlargement of x¼ (b) Enlarge the triangle by a scale factor of enlargement of x 1/3. (c) Enlarge the kite by a scale factor of enlargement of x 1/2. Object B’ Image Object A B A’ Image C C’ Image

10. Enlargements Question 5. Only one of the triangles shown is an enlargement of triangle D. Which triangle is it and what is the scale factor of enlargement? A B C D E Triangle A, scale factor of enlargement is x½

11. Enlargements Question 6. Some of the trapezia shown are enlargements of C. Which ones are they and what is the scale factor of enlargement in each case? A is an enlargement of C by scale factor x 1/3. A B D C E F D is an enlargement of C by scale factor x ½. E is an enlargement of C by scale factor x 2/3.

12. Areas and Volumes Enlargements Areas and Volumes (Extension) 4 3 Area = 12 Investigate what happens to the area of the rectangle shown when it is enlarged by scale factors of enlargement of x2, x3, x4, and x5. Tabulate your results and make a statement. SFx1x2x3x4x5 Dimensions3 x 46 x 89 x 1212 x 1615 x 20 Area units 2 1248108192300 = 12 x 1 2 = 12 x 2 2 = 12 x 3 2 = 12 x 4 2 = 12 x 5 2 The area factor is the square of the scale factor of enlargement.

13. Enlargements 3 2 Investigate what happens to the volume of the cuboid shown when it is enlarged by scale factors of enlargement of x2, x3, x4, and x5. Tabulate your results and make a statement. Volumex1x2x3x4x5 Dimensions1 x 2 x 32 x 4 x 63 x 6 x 94 x 8 x 125 x 10 x 15 Vol units 3 648162384750 = 6 x 1 3 = 6 x 2 3 = 6 x 3 3 = 6 x 4 3 = 6 x 5 3 The volume factor is the cube of the scale factor of enlargement. 1 Areas and Volumes (Extension)

14. Enlargements Question 1. Object A is to be enlarged by a scale factor of enlargement of x2 and object B by a scale factor of enlargement of x 3. Draw and label the images. The points are there to help you with the positioning of the images. B Object A Worksheets

15. Enlargements Question 3. (a) Enlarge the rectangle by a scale factor of enlargement of x¼ (b) Enlarge the triangle by a scale factor of enlargement of x 1/3. (c) Enlarge the kite by a scale factor of enlargement of x 1/2. Object A B C