1 / 7

Chapter 8 – Transformations

Chapter 8 – Transformations. Brian Doherty. Lesson 1 – Transformations. Transformation – A one-to-one correspondence between two sets of points. Isometry – A transformation that preserves distance and angle measure. Lesson 2 – Reflections.

kimama
Download Presentation

Chapter 8 – Transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 – Transformations Brian Doherty

  2. Lesson 1 – Transformations • Transformation – A one-to-one correspondence between two sets of points. • Isometry – A transformation that preserves distance and angle measure.

  3. Lesson 2 – Reflections • Reflection – The reflection of point P through line l is P itself if P is on l. Otherwise, it is the point P’ such that l is the perpendicular bisector of PP’. • Translation – A transformation that is the composite of two successive reflections through parallel lines. • Rotation – A transformation that is the composite of two successive reflections through intersecting lines.

  4. Construction 8 – To Reflect a Point through a Line • Let the point be P and the line be l. With P as center, draw an arc that intersects l in two points, A and B. With A and B as centers, draw two more arcs with the same radius as the first arc. The point in which they intersect, P’, is the reflection of P through l.

  5. Lesson 3 – Isometries and Congruence • Congruent figures – Two figures are congruent if there is an isometry such that one figure is the image of the other. • Glide reflection – A transformation that is the composite of a translation and a reflection in a line parallel to the direction of the translation.

  6. Lesson 4 – Transformations and Symmetry • Rotation symmetry – A figure has rotation symmetry with respect to a point iff it coincides with its rotation image through less than 360˚ about the point. • Reflection symmetry – A figure has reflection (line) symmetry with respect to a line iff it coincides with its reflection image through the line. • Translation symmetry – A pattern has translation symmetry if it coincides with a translation image.

  7. Extra – Dilations • Image – The result of a transformation. • Dilation – A transformation in which the original figure and its image are similar. • Scale factor – In a dilation, the ratio of any length on the image to the corresponding length on the original. • Center of dilation – The point which does not move under a dilation.

More Related