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.

Slides:

Advertisements

Similar presentations

Rotations Warm Up Lesson Presentation Lesson Quiz

Advertisements

7.3 Rotations Advanced Geometry.

Transformations Vocabulary.

Rotations California Standards for Geometry

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.

Rigid Motion in a Plane Reflection

Chapter 7 Transformations. Chapter Objectives Identify different types of transformations Define isometry Identify reflection and its characteristics.

Draw rotations in the coordinate plane.

Geometry Rotations.

Chapter 7 Transformations. Examples of symmetry Lines of Symmetry.

9.5 & 9.6 – Compositions of Transformations & Symmetry

ROTATION. 12/7/2015 Goals Identify rotations in the plane. Apply rotation to figures on the coordinate plane.

Chapter 12.  For each example, how would I get the first image to look like the second?

GEOMETRY HELP DO NOW What is an isometry? What is a rigid motion?

GEOMETRY A CHAPTER 11 ROTATIONS ASSIGNMENT 2 1.What type of transformations are isometries? Reflection, Translation, Rotation, any transformation that.

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.

Rotation Around a Point. A Rotation is… A rotation is a transformation that turns a figure around a fixed point called the center of rotation. A rotation.

MA 08 Geometry 6.9 Rotations.

EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point and what is point symmetry? Rotations.

Geometry Rotations. 2/14/2016 Goals Identify rotations in the plane. Apply rotation formulas to figures on the coordinate plane.

1.4 Rigid Motion in a plane Warm Up

Activation—Unit 5 Day 1 August 5 th, 2013 Draw a coordinate plane and answer the following: 1. What are the new coordinates if (2,2) moves right 3 units?

Unit 10 Transformations. Lesson 10.1 Dilations Lesson 10.1 Objectives Define transformation (G3.1.1) Differentiate between types of transformations (G3.1.2)

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

TransformationsTransformations. transformation One to One Mapping Preimage Point  Image Point A change of position or size of a figure. A  A´

Transformations: Rotations on a Coordinate Plane Meet TED

Symmetry Section 9.6. Line Symmetry  A figure in the plane has line symmetry if the figure can be mapped onto itself by a reflection in a line.  This.

Using Rotations A rotation is a transformation in which a figure is turned about a fixed point. The fixed point is the center of rotation. Rays drawn from.

Transformations involving a reflection or composition of reflections

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

Geometry Rotations.

12-3 Rotations Warm Up Lesson Presentation Lesson Quiz Holt Geometry.

Geometry 4-3 Rotations.

9.5 & 9.6 – Compositions of Transformations & Symmetry

9.4 : Compositions of Transformations

Sect. 7.1 Rigid Motion in a Plane

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

9.4 Compositions of Transformations

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Transformations Chapter 4.

Geometry Rotations.

Bell Ringer 9/18/2018.

Homework Monday 5/23: Rotation of Shapes page 1.

Warm-up ~ Hi! T(2, -3), A(-1, -2) and J(1, 2)

Y. Davis Geometry Notes Chapter 9.

A circular dial with the digits 0 through 9 evenly spaced around its edge can be rotated clockwise 36°. How many times would you have to perform this.

4.3 Rotations Goals: Perform Rotations

9.1 Translations -Transformation: a change in the position, shape, or size of a geometric figure -Preimage: the original figure -Image: the resulting figure.

Geometry: Unit 1: Transformations

Lesson 2.4_Rotation of Shapes about an Origin (0,0)

Rotations Unit 10 Notes.

Starter(s) The coordinates of quadrilateral ABCD before and after a rotation about the origin are shown in the table. Find the angle of rotation. A. 90°

Unit 1: Transformations Day 3: Rotations Standard

7.1 Rigid Motion in a Plane OBJECTIVES:

True or False: Given A(-4, 8), the image after a translation of (x – 7, y + 6) is A’(-11, 14). Problem of the Day.

Warm-up ~ Hi! T(2, -3), A(-1, -2) and J(1, 2)

Unit 4 Transformations.

9.3: Rotations.

Geometry Ch 12 Review Jeopardy

Module 2 Review

Section 4.3 Rotations Student Learning Goal: Students will identify what a rotation is and then graph a rotation of 90, 180 or 270 degrees on a coordinate.

Transformations - Rotations

Rotation Around a Point

Presentation transcript:

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 Twice the distance between the two lines 1/4/2016

Geometry 9-3 Rotations

1/4/2016 Goals Identify rotations in the plane. Apply rotation formulas to figures on the coordinate plane.

1/4/2016 Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation

1/4/2016 Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. Center of Rotation 90  G G’

1/4/2016 A Rotation is an Isometry Segment lengths are preserved Angle measures are preserved Parallel lines remain parallel

Rotations on the Coordinate Plane Know the formulas for: 90  rotations 180  rotations clockwise & counter- clockwise Unless told otherwise, the center of rotation is the origin (0, 0).

1/4/  clockwise rotation Formula (x, y)  (y,  x ) A(-2, 4) A’(4, 2)

1/4/2016 Rotate (-3, -2) 90  clockwise Formula (x, y)  (y,  x) (-3, -2) A’(-2, 3)

1/4/  counter-clockwise rotation Formula (x, y)  (  y, x) A(4, -2) A’(2, 4)

1/4/2016 Rotate (-5, 3) 90  counter-clockwise Formula (x, y)  (  y, x) (-3, -5) (-5, 3)

1/4/  rotation Formula (x, y)  (  x,  y) A(-4, -2) A’(4, 2)

1/4/2016 Rotate (3, -4) 180  Formula (x, y)  (  x,  y) (3, -4) (-3, 4)

1/4/2016 Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw  ABC A(-3, 0) B(-2, 4) C(1, -1)

1/4/2016 Rotation Example Rotate  ABC 90  clockwise. Formula (x, y)  (y,  x) A(-3, 0) B(-2, 4) C(1, -1)

1/4/2016 Rotate  ABC 90  clockwise. (x, y)  (y,  x) A(-3, 0)  A’(0, 3) B(-2, 4)  B’(4, 2) C(1, -1)  C’(-1, -1) A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

1/4/2016 Rotate  ABC 90  clockwise. Check by rotating  ABC 90 . A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

1/4/2016 Rotation Formulas 90  CW(x, y)  (y,  x) 90  CCW(x, y)  (  y, x) 180  (x, y)  (  x,  y) Rotating through an angle other than 90  or 180  requires much more complicated math.

1/4/2016 Compound Reflections If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is the same as a rotation about point P.

1/4/2016 Compound Reflections If lines k and m intersect at point P, then a reflection in k followed by a reflection in m is the same as a rotation about point P. P m k

Compound Reflections Furthermore, the amount of the rotation is twice the measure of the angle between lines k and m. P m k 45  90 

1/4/2016 Compound Reflections The amount of the rotation is twice the measure of the angle between lines k and m. P m k xx 2x 

1/4/2016 Summary A rotation is a transformation where the preimage is rotated about the center of rotation Rotations are Isometries A figure has rotational symmetry if it maps onto itself at an angle of rotation of 180  or less

Homework Page 644 #’s Evens Only