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9-2 Reflections

9-2 Reflections. Reflection Across a Line. Reflection across a line (called the line of reflection ) is a transformation that produces an image with a opposite orientation from the preimage. A reflection is an isometry. Reflecting a Point Across a Line.

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9-2 Reflections

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  1. 9-2 Reflections

  2. Reflection Across a Line • Reflection across a line (called the line of reflection) is a transformation that produces an image with a opposite orientation from the preimage. • A reflection is an isometry.

  3. Reflecting a Point Across a Line • If point P(3, 4) is reflected across the line y = 1, what are the coordinates of its reflection image?  What is the image of the same point P reflected across the line x = -1?

  4. Graphing a Reflection Image • Graph points A(-3, 4), B(0, 1), and C(4, 2). What is the image of ΔABC reflected across the y-axis?  What is the image of ΔABC reflected across the x-axis?

  5. Algebraic Rules for Reflection • Reflection over y-axis. (x,y)-> (-x,y) • Reflection over x-axis. (x,y)-> (x,-y) • Reflection over y=x. (x,y)-> (y,x) • Reflection over y= -x. (x,y)-> (-y,-x)

  6. 9-3 Rotations

  7. Rotation About a Point • A rotation is a transformation that “turns” a figure around point R, called the center of rotation. • The positive number of degrees a figure rotates is the angle of rotation. • A rotation about a point is an isometry. • Unless told otherwise, assume all rotations are counterclockwise.

  8. Rotations of Regular Polygons • The center of a regular polygon is the point that is equidistant from its vertices. • The center and the vertices of a regular n-gon determine n congruent triangles. • Recall that the measure of each central angle can be found by dividing 360 by n. • You can use this fact to find rotation images of regular polygons.

  9. Identifying a Rotation Image • Point X is the center of regular pentagon PENTA. What is the image of each of the following: • 72 rotation of T about X? • 216 rotation of TN about X?  144 rotation of E about X?

  10. Finding an Angle of Rotation • Hubcaps of car wheels often have interesting designs that involve rotation. What is the angle of rotation about C that maps Q to X? What is the angle of rotation about C that maps M to Q?

  11. Algebraic Rules for Rotation • Rotate 900 (x,y)-> (-y,x) • Rotate 1800 (x,y)-> (-x,-y) • Rotate 2700 (x,y)-> (y,-x)

  12. 9-4 Symmetry

  13. Types of Symmetry • A figure has symmetry if there is an isometry that maps the figure onto itself. • A figure has line symmetry (also called reflectional symmetry) if there is a reflection for which the figure is its own image. • The line of reflection is called a line of symmetry; it divides the figure into congruent parts.

  14. A figure has rotational symmetry if there is a rotation of 180 or less for which the figure is its own image. • A figure with 180 rotational symmetry is also said to have point symmetry because each segment joining a preimage with its image passes through the center of rotation.

  15. Identifying Lines of Symmetry • How many lines of symmetry does a regular hexagon have?  How many lines of symmetry does a rectangle have?

  16. Identifying Rotational Symmetry • Does the figure have rotational symmetry? If so, what is the angle of rotation?

  17.  Does the figure have rotational symmetry? If so, what is the angle of rotation? • Does the figure have point symmetry?

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