Year 9 Enlargement Dr J Frost jfrosttiffin kingston

Year 9 Enlargement Dr J Frost (jfrost@tiffin. kingston. sch. uk) Last modified: 2 nd November 2014

8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 ROTATE Warning: Pressing this button may result in death or loss of limbs. REFLECT Warning: Pressing this button may result in bowel problems. TRANSLATE Warning: Do not press if you are pregnant or suffer -6 from a heart condition. ENLARGE Warning: Pressing this button may result in loss of girlfriend. N

Starter y 4 Describe the transformations that resulted in the 3 images. Object 2 (If you finish, can you describe the transformation resulting in Image A using only reflections? ) x -5 4 -4 5 3 1 -3 6 -2 Image A -1 -1 -2 -3 -4 0 1 Image B Image C 2 3

Describing an Enlargement y 4 It’s becoming 2 times as wide. 3 Image 2 1 Object x -5 4 -4 5 It’s becoming 4 times in size in terms of area. -3 6 -2 -1 0 1 2 -1 It’s being enlarged about some point. Clearly this shape is being ‘enlarged’ in some way. What two things might describe such a transformation? -2 -3 -4 Click to Start Bromanimation 3

Describing an Enlargement y 4 3 . . . by a scale factor of 2. Image 2 1 Object x -5 4 -4 5 -3 6 -2 -1 -1 An enlargement about the point (-5, -1) -2 -3 -4 0 1 2 3

Example 1 y 4 Describe enlargement from A to B. 3 B 2 The centre of enlargement. A x -5 4 -4 5 -3 6 1 -2 -1 0 1 2 -1 The distance from the centre is being tripled, so we have enlargement by a scale factor of 3. -2 -3 “Enlargement about the point (-3, 1) by a scale factor of 3. ” -4 3

Example 2 y 4 Describe enlargement from A to B. 3 A 2 B x -5 4 -4 5 -3 6 1 -2 -1 -1 -2 -3 -4 0 1 2 3

Test Your Understanding y 4 Describe enlargement from A to B. 3 2 B 1 x -5 4 -4 5 -3 6 -2 -1 -1 -2 -3 -4 0 A 1 2 3

Drawing an Enlargement y 4 Enlarge the shape by a scale factor of 2 about the point (0, -2) 3 2 1 x -5 4 -4 5 -3 6 -2 Image -1 -1 0 1 2 Object -2 -3 The approach is to take each vertex on the object one at a time, count the -4 squares across and up/down from the centre, and times each by the scale factor 3

Example 4 y 4 3 2 1 Image x -5 4 -4 5 -3 6 -2 -1 -1 Object -2 -3 -4 0 1 2 3

Test Your Understanding y 4 3 2 1 Object x -5 4 -4 5 -3 6 -2 -1 -1 Image -2 -3 -4 0 1 2 3

Negative Enlargement y 4 Enlarge the shape by a scale factor of -1 about the point (0, 2) 3 2 Image 1 x -5 4 -4 5 -3 6 -2 Object -1 0 1 2 -1 -2 -3 -4 the principle is exactly the same. Any Bro Tip: When the scale factor is negative, ‘negative distances’ go in the opposite direction. 3

Test Your Understanding y 4 3 2 1 Object Image x -5 4 -4 5 -3 6 -2 -1 0 1 -1 -2 -3 Enlarge the shape by a scale factor of -2 about the point (1, 1) -4 2 3

Test Your Understanding y 4 3 2 Image 1 x -5 4 -4 5 -3 6 -2 Object -1 0 1 2 -1 -2 -3 Enlarge the shape by a scale factor of -0. 5 about the point (0, 2) -4 3

Test Your Understanding y 4 3 2 1 Object Image x -5 4 -4 5 -3 6 -2 -1 0 1 2 -1 -2 -3 -4 Enlarge the shape by a scale factor of -1. 5 about the point (1, 1) 3

Worksheet Time

Answers

Answers

Answers Enlargement of scale factor 2? about the origin.

Answers B

Answers

Answers Enlargement by a scale factor? of 3 about the origin.

Answers Enlargement of scale factor 3 ? about the origin.

Recap y 4 3 2 Object 1 Image x -5 4 -4 5 -3 6 -2 -1 0 1 -1 -2 -3 ? ? -4 ? 2 3

Recap y 4 3 2 Object 1 Image x -5 4 -4 5 -3 6 -2 -1 0 1 -1 -2 -3 ? ? -4 ? 2 3

Year 9 Combined Transformations Dr J Frost (jfrost@tiffin. kingston. sch. uk) Last modified: 5 th October 2013

Starter y 4 (Draw this in your book!) Rotate this object 90 clockwise about the origin, then reflect in the line y = x. How could we have done the same with just one transformation? x -5 4 -4 5 -3 6 Object 3 Final Image 2 1 -2 Image after rotation -1 -1 -2 -3 -4 0 1 2 3

y 4 On the same axes, now reflect the object in the y axis followed by the x axis. Again, how could we have done the same with just one transformation? x -5 4 -4 5 Object 3 2 1 -3 6 -2 -1 0 -1 -2 -3 -4 Final Image 1 2 3

y 4 Sketch the following in your books. List the sequence of two transformations which results in the image. 3 2 Object x -5 4 -4 5 -3 6 1 -2 -1 -1 -2 -3 -4 0 1 2 Image 3

y 4 Work in pairs: Both sketch the following in your book. Pick a reflection and a rotation of your choice*, sketch the image, then get your neighbour to try and work out the transformations you choose from the image. 3 2 Object 1 x -5 4 -4 5 -3 6 -2 -1 0 1 2 -1 -2 -3 -4 *Although to keep things simple, the line of reflection must be in the form x = c, y = x or y = -x 3