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TRANSFORMATIONSObjective: To identify isometries To find reflection
images of figures
ReflectionTranslation
TRANSFORMATIONS
Rotation Dilation
A reflection produces a mirror image of a figure along a line of reflection.
A translation moves every point on a figure the same distance in the same direction.
A rotation turns a shape about a fixed point. To perform a rotation, three details are needed: 1) The center 2) The angle of rotation and 3) The direction of rotation
A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape.
IMPORTANT TERMS Isometry - A transformation that does not change the shape or size of a figure. In other words, it preserves lengths, angle measures, parallel lines, and distance between points.
Pre-image - the figure prior to the transformation
Image – the figure after the translation
TRANSLATIONS-SLIDE! To translate a shape every point must move:the same distanceIn the same direction
How would you write a rule for the translation shown to the right?
Pre-Image Image
EXAMPLE #1
ROTATIONS-TURN!"Rotation" means turning around a center.
The distance from the center to any point on the shape stays the same
Go counter-clockwise
COUNTER CLOCKWISE
PREIMAGE [Before]
IMAGE [After]
Amount of turn: Point of rotation:Direction:
EXAMPLE #2
REFLECTIONS-FLIP!
A reflection is a transformation in which the figure is the mirror image of the other. Notice that in each case, the pre-image is always the same distance away from the line of reflection as the image. Very important!
LINES OF SYMMETRY The x-axis
The y-axis
The line
Any horizontal line [HOY] y=any
number
Any vertical line [VUX] x=any
number
EXAMPLE #3
DILATIONS-GROW OR SHRINK!A dilation enlarges or reduces the size of a shape; this is why the pre-image and image of a dilation are not congruent, but similar.
Every dilation has a center point and a scale factor.
EXAMPLE #4