1. Transformations of Shapes Translation by a vector Stretches Rotations around a point Reflections in the x- and y- axis Reflections in the line y = x and y = -x

2. Translations Reflections Stretches Rotations

3. Translations

4. www.le.ac.uk Translate by a vector: -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 Return

5. Stretches We stretch shapes parallel to the x- and y-axis. We can stretch a shape in both the x- and y- axis, or even stretch in both axis at the same time. If we stretch by a number bigger than one, the shape gets bigger. If we stretch by a number less than one, the shape gets smaller. Try it out for yourself!

6. Stretch in the x and y direction by: x by y by -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

7. Rotations To define a rotation we need to pick a point to rotate around. We also need to choose an angle to rotate by. Try it out for yourself on the next slide. What shape does the rotation move around on? Just pick an x- and y- coordinate and then move the slider to change the angle.

8. Rotate by degrees. x co-ordinate of rotation. y co-ordinate of rotation. -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

9. Reflections There are many different types of reflections. We can reflect in the x- and y- axis, but also in the lines x = a or y = a, where a is just some number. We can also have reflections in the line y = x and y = -x. In the next few slides you will have a play with these different concepts. First investigate reflections in the x- and y- axis.

10. Reflections in x- and y- axis For the next exercise you should choose a co- ordinate to plot the square at. Then by simply pressing one of the two buttons, the required reflection is drawn. The red line represents the axis being reflected along.

11. www.le.ac.uk x y -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

12. Reflection in the lines y = a or x = a. For the next exercise you should choose a co- ordinate to plot the square at. You should then choose which line you would like to reflect along. The red line represents the line being reflected along.

13. reflect in the line x = x y -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

14. reflect in the line y = x y -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

15. Reflection in the lines y = x or y = -x. For the next exercise you should choose a co- ordinate to plot the square at. You will then press the button to reflect the shape in either of the lines y = x or y = -x. The red line represents the line being reflected along. The blue square is the reflected shape.

16. x y -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

17. x y -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

18. Enlargements To enlarge a shape we require a point to enlarge around, and a scale factor. In the next two pages, you will choose a point to enlarge, and a scale factor. You will get to try it out on the next two slides using a triangle and a square. What do you notice if you have a negative scale factor?

19. x y x y enlargement factor -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return

20. x y xy enlargement factor -2-4-6-8-10246810 2 4 6 8 -2 -4 -6 -8 Return