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Reflections

Reflections. What will we accomplish in today’s lesson?. Given a pre-image and its reflected image, determine the line of reflection. Given a pre-image and its reflected image graphed on the coordinate plane, determine the line of reflection and give a function rule for the reflection.

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Reflections

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  1. Reflections

  2. What will we accomplish in today’s lesson? • Given a pre-image and its reflected image, determine the line of reflection. • Given a pre-image and its reflected image graphed on the coordinate plane, determine the line of reflection and give a function rule for the reflection. • Given the line of reflection, draw a reflection on plain paper. • Given a horizontal or vertical line of reflection or function rule, draw a reflection on the coordinate plane. Reflections • A reflection is a transformation that flips a figure across a line, called the line of reflection. • Segments connecting corresponding points of a pre-image and its reflected image are bisected by the line of reflection. • Corresponding points of a pre-image and its reflected image are equidistant from the line of reflection. • The reflection of a figure changes orientation so that it faces in the opposite direction of the original figure.

  3. What is a reflection? • A reflection is a transformation that flips a figure over a line called the line of reflection. • A reflection is a type of rigid transformation. line of reflection (the x-axis in this example)

  4. Properties of Reflections • Segments connecting corresponding points of a pre-image and its reflected image are bisected by the line of reflection.

  5. Properties of Reflections • Corresponding points of a pre-image and its reflected image are equidistant from the line of reflection. • The reflection of a figure changes orientation so that it faces in the opposite direction of the original figure.

  6. Coordinate notation for reflections in the coordinate plane 3 rules for reflections in a coordinate plane • reflection across the x-axis: (x, y)  (x, -y) • reflection across the y-axis: (x, y)  (-x, y) • reflection across the line y=x: (x, y)  (y, x)

  7. Reflect the following figure across the x-axis pre-image points (1,1) (4,1) (4,4)

  8. Reflect the following figure across the y-axis

  9. Reflect the following figure across the line y=x pre-image points (-3,2) (-1,2) (-1,5)

  10. Options for the line of reflection • A reflection can occur across any line. • It is not limited just to the x-axis, y-axis, and line y=x.

  11. Identifying the equation for the line of reflection helps to see the change between the coordinates of the pre-image and image. The line of reflection is represented by the equation x = -2. To begin, find the distance from the pre-image point to the line of reflection.  Each image point must be that same distance in the opposite direction from the line of reflection.  For example, point A is 3 units from the line of reflection.  So A' must be three units in the opposite direction from the line of reflection. 

  12. Reflect the figure across the line x=2 pre-image points (1,4) (1,1) (0,1)

  13. Reflect the line across y=3 pre-image points (7,3) (-1,7) (1,4) (6,3)

  14. Try it yourself! • http://www.shodor.org/interactivate/activities/Transmographer/

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