Reflections
1. Reverses orientation
2. A reflection or an isometry
Transformation- change in position, shape or size of a figure
Ismetry- transformation in which one preimage is congruent image
Orientation- position
Section 3-2
Translations
Translation- a transformation that moves points the same distance and in the same direction
Properties of Translation
1. A translation is an isometry
2. A translation doesnt change direction
Section 3-3
Rotation
Rotaion is based on:
1. Center of rotation (vertex point, point not on polygon, line, etc,)
2. What direction you are going to rotate (clockwise or counter clckwise)
3. Angle of rotation (how far you are going)
Clockwise is negative values
Counter clockwise is positive values
Rotation- A rotation of x degrees about point R is a transformation such that for any point V, its image is the point V'
Where RV=RV' and m
Properties
1. Property of rotations is an isometry
2. Orientation doesn't change
Section 3-4
Composition of reflections
Theorem 3-1: a composition of reflections in two parallel lines is a translation
Theorem 3-2: a composition of reflections in two intersecting lines is a rotation
Theorem 3-3: in a plane, two congruent figures can be mapped into one another by a composition of at least three reflections
Glide reflections- a composition of three reflections in lines that intersect in more than one point
x= reflecting over vertical line
y= reflecting over a horizontal line
Theorem 3-4 Isometry Classification: there are only four isometries they are the following;
reflection, translation, rotation and glide reflection
Section 3-5
Symmetry
Symmetry- an isometry that maps a figure to itself
Rotational Symmetry- a figure has roational symmetry if there was a rotation
of 180 degrees or less that maps the figure onto itself.
Section 3-6
Tesselations
Tesselation- a repeating pattern of figures that completely covers a plane without gaps or overlaps
Theorem 3-5: every triangle tesselates
Theorem 3-6: every quadrilateral tesselates
Symmetry- an isometry that maps a figure onto itself
Translational symmetry- maps tesselation onto itself
Glide Reflectional symmetry- a glide reflect, maps tesselation onto itself
Rotational point symmetry- point has to be 180 Degrees- rotation under 180 degrees, maps tesselation onto itself
Section 3-7
Dilation
Dilation- with center cond scale factor for n, where n>o, maps a point R to R' in such a way that R' is on ray CR and
CR'=n(CR) The center of a dilation is on its own image. If n>1, the dilation is an enlargement. If O i s less than n and n is less than 1, the dilation is a
reduction.
