Report

1 Real-life reflections Animation Architecture Graphic Design 2 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”. A' • 4 •A 3 2 1 -2 -1 0 1 2 3 Reflection Tell whether the red figure is a reflection of the blue figure. This figure is a reflection. This figure is not a reflection. 4 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. Reflecting a Polygon 1. 2. 3. 4. 5. 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. Example Reflecting in the y-Axis Preimage Image Coordinates of each vertex of the triangle and its image. Pre-image Image (-3, -2) (-10, 0) (-2, 3) (3, -2) (10, 0) (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 8 Reflecting in the x-Axis Coordinates of each vertex of the triangle and its image. Pre-image (-2, 2) (-1, 7) (6, 5) Image (-2, -2) (-1, -7) (6, -5) Notice that when a point is reflected over the x-axis, its y-coordinate is multiplied by -1. 9 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. 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. Algebra Pre-image Image (x, y) (-x, y) 11 Your turn! Graph the triangle with vertices J(0, 1), K(1, 4), and L( 5, 2). Reflect the triangle in the y-axis. 12 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. 13