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Reflections

Reflections. Real-life reflections. Animation Architecture Graphic Design. Reflections. A reflection creates a mirror image of each point of a figure. A reflection is a transformation , an operation that changes a figure into another figure. The new

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Reflections

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  1. Reflections

  2. Real-life reflections Animation Architecture Graphic Design

  3. Reflections • A reflection creates a mirror image of each point of a figure. • A reflection is a transformation, an operation that • changes a figure into another figure. The new • figure created is called the image. • Notation: A A' is read • “A goes to A prime”.  4 3 2 1 A'• • A -2 -1 0 1 2

  4. Reflection • Tell whether the red figure is a reflection of the blue figure. This figure is a reflection. This figure is not a reflection.

  5. Reflections • A reflection is a transformation in which a figure is flipped over a line of reflection. This line can be thought of as a mirror in which the image is a reflection of the pre-image. • For this class, our line of reflection will be either the x-axis or the y-axis on a coordinate grid.

  6. Reflecting a Polygon • Determine the line of reflection (x or y axis). • Find the distance from the vertex of the polygon to the line of reflection. • Mark the image of the vertex the same distance from the line of reflection, but in the opposite direction. • Continue steps 2-3 until all vertices have been reflected. • Draw the image by drawing line segments connecting adjacent vertices.

  7. Example

  8. Reflecting in the y-Axis Coordinates of each vertex of the triangle and its image. Pre-image Image Preimage Image (-3, -2) (3, -2) (-10, 0) (10, 0) (-2, 3) (2, 3) Notice that when a point is reflected over the y-axis, its x-coordinate is multiplied by -1. http://staff.argyll.epsb.ca/jreed/math9/strand3/transformations.htm

  9. Reflecting in the x-Axis Coordinates of each vertex of the triangle and its image. Pre-image Image (-2, 2) (-2, -2) (-1, 7) (-1, -7) (6, 5) (6, -5) Notice that when a point is reflected over the x-axis, its y-coordinate is multiplied by -1.

  10. Conjecture • A proposition or conclusion that is based on limited evidence. • Example: Bats have wings and can fly. Eagles have wings and can fly. A Pegasus has wings and can fly. Conjecture: Any animal with wings can fly.

  11. Reflections • Reflection across the x-axis • Words To reflect a point across the x-axis, multiply its y-coordinate by -1. Pre-image Image Algebra(x, y) (x, -y) • Reflection across the y-axis • Words To reflect a point across the y-axis, multiply its x-coordinate by -1. Pre-image Image Algebra (x, y) (-x, y)

  12. Your turn! Graph the triangle with vertices J(0, 1), K(1, 4), and L( 5, 2). Reflect the triangle in the y-axis.

  13. Your turn! Graph the quadrilateral with vertices S(-3,2), T(-1, 4), U(-4, 5), and V(-5, 3). Reflect the quadrilateral in the x-axis.

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