Sarah's Transformation Web
Reflections
Reflections

Reflections

The reflection of a point A over a line m is:

  • the point A, if A is on m;
  • the point A' such that m is the perpendicular bisector of the line -AA'-, if A is not on m.

    Examples: (instead of all the points on this face to show the reflections algebraically and arithmetically, the point (6.5,10), which is the point on the top of his head, will be used.)

    GEOMETRICALLY

    F' is the reflection image over the y-axis. F'' is the reflection image over the x-axis.

    ALGEBRAICALLY

    reflection over the x-axis
    rx (6.5,10) = (6.5,-10)

    reflection over the y-axis
    ry (6.5,10) = (-6.5,10)

    ARITHMETICALLY

    reflection over the x-axis

    [[1  0]   *  [[6.5]  =  [[6.5]
 [0 -1]]      [10]]      [-10]]

    reflection over the y-axis

    [[-1 0]   *  [[6.5]  =  [[-6.5]
  [0 1]]      [10]]        [ 10]]
    NOTE: items usually in subscript will be represented in italics on these pages
    by Sarah : turnip@alaska.net -------Last Revised 09/09/96