1 / 10

Understanding Geometric Transformations: Types and Rules Explained

This lesson covers the essential concepts of geometric transformations, including translations, reflections, and rotations. Students will learn how transformations change the position of shapes on a coordinate plane and how to apply specific rules for each type of transformation. Key elements include identifying the relationship between pre-images and images, finding angles, and solving for variables. The focus is on understanding how to apply transformation rules to points and shapes effectively, enhancing comprehension of geometric principles.

zhen
Download Presentation

Understanding Geometric Transformations: Types and Rules Explained

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. GROUPS!!! #1: Ateia, Sa’sha, Xzavier #2: JJ, Mya, Keionna #3: Mary, Robbie, Ky’Asia #4: Kanari, Ty’Asia, Catwan #5: Kayla, Laquana, Shelby #6: Courtney, Kamecia, Justin

  2. DO NOW!!! What type of transformation is displayed in the figure to the left? What is the rule for how the shape is transformed? How are the two triangles related? DO NOW!!! 1) Find angle #2. 2) Solve for “x”.

  3. Geometric Transformations • A transformation changes the position of a shape on a coordinate plane • 3 main types of transformations: 1. translations 2. rotations 3. reflections

  4. A type of transformation that moves a point, line, or shape up/down and side to side. • Translations preserve shape. Translations move objects, but do not change them. Translation

  5. Transformations • Pre-image: the original image (ex: ∆ABC) • Image: The image after the transformation(ex: ∆A’B’C’)

  6. Reflection • A reflection flips a figure over a line. y x

  7. Special Reflections Rules (x, y )  (x, -y) • Reflection across x– axis: • Reflection across y – axis: • Reflection over origin: • Reflection over line y = x: • APPLY THESE RULES TO ALL POINTS ON THE SHAPE BEING REFLECTED!!! (x, y )  (-x, y) (x, y )  (-x, -y) (x, y )  (y, x)

  8. Rotation • A transformation in which a figure is turned about a fixed point, called the center of rotation.

  9. COUNTERCLOCKWISE ROTATION RULES 90 degrees counterclockwise around origin:(x, y) (-y, x) 180 degrees around the origin: (x, y)  (-x, -y) 270 degrees counterclockwise around origin: (x, y) (y, -x) APPLY THESE RULES TO ALL POINTS ON THE SHAPE BEING ROTATED!!!

  10. ROTATION RULES CLOCKWISE 90 degrees clockwise around origin:(x, y) (y, - x) 180 degrees around the origin: (x, y)  (-x, -y) 270 degrees clockwise around origin: (-y, x) APPLY THESE RULES TO ALL POINTS ON THE SHAPE BEING ROTATED!!!

More Related