Geometry Glide Reflections and Compositions. Goals Identify glide reflections in the plane. Represent transformations as compositions of simpler transformations.

Slides:

Advertisements

Similar presentations

7.5 Glide Reflections and Compositions

Advertisements

Honors Geometry Transformations Section 1 Reflections.

The original figure is called the preimage.

1-7 Warm Up Lesson Presentation Lesson Quiz

Compositions of Transformations

(For help, go to Lessons 12-1 and 12-2.) Given points R(–1, 1), S(–4, 3), and T(–2, 5), draw RST and its reflection image in each line. 1.the y-axis 2.

Geometry Ch 12 Review Jeopardy Definitions Name the transformation Transform it!Potpourri Q $200 Q $400 Q $600 Q $800 Q $1000 Q $200 Q $400 Q $600 Q $800.

Reflections Section 9.3.

Rigid Motion in a Plane Translations and Reflections Glide Reflections

Draw rotations in the coordinate plane.

Isometries Page Isometry – A transformation in a plane that results in an image that is congruent to the original object. Which transformations.

Section 9.5. Composition of Transformations When two or more transformations are combined to form a single transformation, the result is a composition.

Bell Work (Have out 7.4s) Sketch a triangle with vertices A (-1, -3), B (1, -1), C (-1, 0). Then sketch the image of the triangle after the translation.

COMPOSITIONS OF TRANSFORMATIONS

9.5 & 9.6 – Compositions of Transformations & Symmetry

12.1 – Reflections 12.5 – Symmetry M217 – Geometry.

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Identify reflections, rotations, and translations. Graph transformations in the coordinate.

Compositions of Transformations

9.1 – Translate Figures and Use Vectors

LESSON 5-1 I can draw reflected images. I can recognize and draw lines of symmetry.

Section 7.3 Rigid Motion in a Plane Rotation. Bell Work 1.Using your notes, Reflect the figure in the y-axis. 2. Write all the coordinates for both the.

Review from Friday The composition of two reflections over parallel lines can be described by a translation vector that is: Perpendicular to the two lines.

1.8 Glide Reflections and Compositions Warm Up Determine the coordinates of the image of P(4, –7) under each transformation. 1. a translation 3 units left.

 Composition of Transformation- 2 or more transformations are combined to form a single transformation  The composition of 2 (or more) isometries is.

Rotations 7.4 Rotations 7.4 Chapter 7 Section 7.4 Translations.

7.5 Composition Transformations California Standards for Geometry 17: Prove theorems using coordinate geometry 22: Know the effect of rigid motions on.

COMPOSITIONS WITH TRANSFORMATIONS. COMPOSITIONS Definition: The nesting of two or more processes to form a single new rule. Composition of Transformations.

DRILL 1) If A is in between points B and C and AC is 4x + 12 and AB is 3x – 4 and BC is 57 feet how long is AB? 2) Angles A and B are Supplementary if.

Warm Up Week 1. Section 7.2 Day 1 I will identify and use reflections in a plane. Ex 1 Line of Reflection The mirror in the transformation.

Translations 12-2 Warm Up Lesson Presentation Lesson Quiz

Go Back > Question 1 Describe this transformation. A reflection in the line y = x. ? Object Image.

Chapter 9 Properties of Transformations Warren Luo Matthew Yom.

Compositions of Transformations

9-4 Compositions of Transformations You drew reflections, translations, and rotations. Draw glide reflections and other compositions of isometries in the.

Compositions of Transformations

1.Fill in the blanks with always, sometimes, or never. a)A rotation is _____ an isometry. b)An isometry is _____ a reflection. c)An isometry is _____ a.

7.4 Translations and Vectors June 23, Goals Identify and use translations in the plane. Use vectors in real- life situations.

Holt Geometry 1-7 Transformations in the Coordinate Plane Warm Up 1. Draw a line that divides a right angle in half. 2. Draw three different squares with.

Transformations involving a reflection or composition of reflections

Honors Geometry Transformations Section 3 Translations and Compositions.

9-4 Compositions of Isometries. Isometry: a transformation that preserves distance or length (translations, reflections, rotations) There are 4 kinds.

9-4 COMPOSITIONS OF ISOMETRIES. Isometries Isometry: transformation that preserves distance, or length. Translations, reflections, and rotations are isometries.

 Complete the Summary of Transformations handout. Translation of h units horizontally and y units vertically Reflection over the y-axis Reflection over.

Check It Out! Example 1 a.b. Yes, the figures are similar and the image is not turned or flipped. No, the figures are not similar. Tell whether each transformation.

Geometry 4-3 Rotations.

Chapter 9 Vocab Review.

Section 12-4 Compositions of Reflections SPI 32D: determine whether the plane figure has been translated given a diagram.

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

9.4 Compositions of Transformations

Transformations.

Glide Reflections and Compositions

Compositions of Transformations

Compositions of Transformations Symmetry

Multiple Transformations

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

DRILL If A is in between points B and C and AC is 4x + 12 and AB is 3x – 4 and BC is 57 feet how long is AB? Angles A and B are Supplementary if.

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

9.3: Compositions of Transformations

Geometry PreAP, Revised ©2013 1–7 and 12–1: Transformations

Composition of Transformations

Bellwork Complete the Reflections worksheet on the counter

Warm up Dilate P(-12, -12) using Rotate Q(-1, -3) 90

8th Grade: Chapter 6 TRANSFORMATIONS

Warm up Rotate P(-4, -4) 180 Rotate Q(-1, -3) 90 CCW

Identify and graph compositions of transformations, such as glide reflections LT 12.4.

Glide Reflections and Compositions

Multiple Transformations

Transformations - Rotations

Objectives Apply theorems about isometries.

Presentation transcript:

Geometry Glide Reflections and Compositions

Goals Identify glide reflections in the plane. Represent transformations as compositions of simpler transformations.

Glide Reflection A glide reflection is a transformation where a translation (the glide) is followed by a reflection. Line of Reflection

Glide Reflection 1.A translation maps P onto P’. 2.A reflection in a line k parallel to the direction of the translation maps P’ to P’’. Line of Reflection 3 12

Example Find the image of  ABC after a glide reflection. A(-4, 2), B(-2, 5), C(1, 3) Translation: (x, y)  (x + 7, y) Reflection: in the x-axis

Find the image of  ABC after a glide reflection. A(-4, 2), B(-2, 5), C(1, 3) Translation: (x, y)  (x + 7, y) Reflection: in the x-axis (-4, 2) (-2, 5) (1, 3)

Find the image of  ABC after a glide reflection. A(-4, 2), B(-2, 5), C(1, 3) Translation: (x, y)  (x + 7, y) Reflection: in the x-axis (-4, 2) (-2, 5) (1, 3) (5, 5) (3, 2) (8, 3)

Find the image of  ABC after a glide reflection. A(-4, 2), B(-2, 5), C(1, 3) Translation: (x, y)  (x + 7, y) Reflection: in the x-axis (-4, 2) (-2, 5) (1, 3) (5, 5) (3, 2) (8, 3) (5, -5) (3, -2) (8, -3)

Find the image of  ABC after a glide reflection. A(-4, 2), B(-2, 5), C(1, 3) Translation: (x, y)  (x + 7, y) Reflection: in the x-axis (-4, 2) (-2, 5) (1, 3) (5, 5) (3, 2) (8, 3) (5, -5) (3, -2) (8, -3) Glide Reflection

You do it. Locate these four points: M(-6, -6) N(-5, -2) O(-2, -1) P(-3, -5) Draw MNOP M N O P

You do it. Translate by  0, 7 . M N O P M N O P

You do it. Translate by  0, 7 . M N O P M’ N’ O’ P’

You do it. Reflect over y-axis. M N O P M’ N’ O’ P’ M’’ N’’ O’’ P’’

Compositions A composition is a transformation that consists of two or more transformations performed one after the other.

Composition Example A B 1.Reflect AB in the y-axis. 2.Reflect A’B’ in the x-axis. A’ B’ A’’ B’’

Try it in a different order. A B 1.Reflect AB in the x-axis. 2.Reflect A’B’ in the y-axis. A’ B’ A’’ B’’

The order doesn’t matter. A B A’ B’ A’’ B’’ A’ B’ This composition is commutative.

Commutative Property a + b = b + a = ab = ba 4  25 = 25  4 Reflect in y, reflect in x is equivalent to reflect in x, reflect in y.

Are all compositions commutative? Rotate RS 90  CW. Reflect R’S’ in x-axis. R S R’ S’ R’’ S’’

Reverse the order. Reflect RS in the x-axis. Rotate R’S’ 90  CW. R S R’ S’ R’’ S’’ All compositions are NOT commutative. Order matters!

Compositions & Isometries If each transformation in a composition is an isometry, then the composition is an isometry. A Glide Reflection is an isometry.

Example Reflect MN in the line y = 1. Translate using vector  3, -2 . Now reverse the order: Translate MN using  3, -2 . Reflect in the line y = 1. M N Both compositions are isometries, but the composition is not commutative.

Summary A Glide-Reflection is a composition of a translation followed by a reflection. Some compositions are commutative, but not all.