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