Chapter 8: Transformations

1. Chapter 8:Transformations By Yujie Jenny Ma

2. Lesson 1 Vocabulary: • Transformation – a one-to-one correspondence between two sets of points • Pre-image – the original figure • Image – figure after transformation

3. Vocabulary cont’d • Center of dilation – the point which is used as a reference point for a dilation • Line of reflection – the mirror; the line over which an image is reflected • Isometry – a transformation that preserves distance and angle measure

4. Translation – a slide; a transformation where all the points in the image are the same distance from their corresponding points in the pre-image

5. Reflection – a transformation where all points on the image are the same distance from the line of reflection as their corresponding points in the pre-image

6. Rotation – a transformation where a figure is shifted by an angle around a specified point

7. Dilation – a transformation where a figure is increased or decreased in size by a factor (the points of the image are at the distance of their corresponding points, on the pre-image, from the center of dilation multiplied by the factor)

8. Lesson 2 • A reflection through line l of point P creates P’. Line l is then the perpendicular bisector of segment PP’.

9. Construction 8 – reflecting a point across a line

10. Defining other transformations through reflections • Translation – the composite of two successive reflections through parallel lines • Rotation – the composite of two successive reflections through intersecting lines • Center of rotation – the point about which a rotation occurs • Magnitude – the measure of the angle through which a point of the original figure turns to coincide with its rotation image

11. Lesson 3 Vocabulary: • Congruent – two figures are such if there exists an isometry such that one figure is the image of the other • Glide Reflection – the composite of a translation and a reflection over a line parallel to the direction of the translation (in a sense, three or some greater odd number of reflections) • Mirror Image – created by an odd number of reflections, two figures are the reverse of one another

12. Glide Reflection

13. They’re congruent.

14. Lesson 4 Vocabulary: • Rotation symmetry – a figure possesses this characteristic, with respect to a point, iff it coincides exactly with its rotation image when rotated less than 360˚ about the specific point (the center of the figure is usually said point) • A figure has point symmetry if it looks exactly the same turned upside down • n-fold rotation symmetry – a figure has this iff the smallest angle through which it can be turned to look exactly the same is 360˚/n • A figure with point symmetry has 2-fold symmetry

15. Vocabulary cont’d • Reflection (line) symmetry – a figure has this, with respect to a line, iff it coincides with its reflection image through the line • The line is sometimes called the axis • Translation symmetry – a patter has such iff it coincides with a translation image

16. Rotation symmetry

17. Reflection symmetry

18. Translation symmetry