TRANSFORMATIONS - DEFINITIONS 1.Line of Reflection 2.Translation Vector 3.Center of Rotation 4.Angle of Rotation 5.Composition of Transformations 6.Symmetry 7.Rotational Symmetry 8.Center of Symmetry 9.Order of Symmetry 10.Dilations Honesty is the first chapter in the book of wisdom. Thomas Jefferson. Objective: To be able to identify geometric reflections, and to recognize and draw lines and points of symmetry.

NOTEBOOK 10% of overall grade Four Sections Glossary Processes & Procedures (notes, examples) Daily Work (homework) Assessments (Quizzes, tests) Arranged from Oldest to Newest All Definitions need to be completed at time of a Notebook Check You are expected to keep all materials in your notebook until Midterm!

CHAPTER 9 Transformations

STANDARDS 9.1 Reflections Check.3.5, Check.3.6, CLE , CLE , Spi.3.3, Spi TranslationsCLE , CLE , Spi RotationsCLE , CLE , Spi Compositions of Transformations with Lab Check.4.31, Check.4.33, Check.4.34, CLE SymmetryCheck.4.32, CLE DilationsCLE , CLE , Spi.3.3

REFLECTIONS Chapter 9.1 CLE Explore the effect of transformations on geometric figures and shapes in the coordinate plane. CLE Apply the major concepts of transformation geometry to analyzing geometric objects and symmetry. Spi.3.3 Describe algebraically the effect of a single transformation (reflections in the x- or y-axis, rotations, translations, and dilations) on two- dimensional geometric shapes in the coordinate plane.

REFLECTIONS Reflection across a line. Segment connecting a point and its image is perpendicular to the line of reflection. ABCDE corresponds to A’B’C’D’E’ Since E is on the line of reflection E and E’ are the same point. A B C D E A’ B’ C’ D’ m

EXAMPLE 1 Draw the reflected image of quadrilateral ABCD in line n. A.B. C.D.

REFLECTIONS ABOUT A POINT  UVW   U’V’W’  VWX   V’W’X’  WXY   W’X’Y’  XYZ   X’Y’Z’  YZU   Y’Z’U’  ZUV   Z’U’V’ U V W X Y Z V’ W’ X’ U’ Z’ Y’ UV  U’V’ VW  V’W’ WX  W’X’ XY  X’Y’ YZ  Y’Z’ UZ  U’Z’

REFLECTION IN THE X AXIS K(2, -4), L(-1, 3) M(-4, 2), N(-3, -4) Reflection K’(2, 4) L’(-1, -3) M’(-4, -2) N’(-3, 4) Multiply y coordinate by -1

REFLECTION IN THE Y AXIS K(2, -4), L(-1, 3) M(-4, 2), N(-3, -4) Reflection K’(-2, -4) L’(1, 3) M’(4, 2) N’(3,-4) Multiply x coordinate by -1

REFLECTION IN THE ORIGIN K(2, -4), L(-1, 3) M(-4, 2), N(-3, -4) Reflection K’(-2, 4) L’(1, -3) M’(4, -2) N’(3,4) Multiply x & y coordinate by -1

REFLECTION IN THE LINE Y=X K(2, -4), L(-1, 3) M(-4, 2), N(-3, -4) Reflection K’(-4, 2) L’(3, -1) M’(2, -4) N’(-4, -3) Interchange x and y coordinates

USING REFLECTIONS Cannot Shoot directly Plan shot so that the reflection of the angle rebounds the ball into the hole Line of Symmetry or Mirror Line

EXAMPLE 3 A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1), C(1, –2), and D(3, 0). Graph ABCD and its image over x = 2. A.B. C.D.

SUMMARY  Reflection across a line, segment connecting a point and its image is perpendicular to the line of reflection.  ABCDE corresponds to A’B’C’D’E’  Reflect in X axis …Multiply y coordinate by -1  Reflect in Y axis …Multiply x coordinate by -1  Reflect in Origin …Multiply x & y coordinate by -1  Reflect in line y = x …Swap x and y coordinates