Whiteboardmaths.com © 2010 All rights reserved

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 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.

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

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

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

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

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 x½

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’

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

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

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.

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 = 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.

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 = 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)

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

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