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Transformations

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by

Annabel Beckett

on 10 February 2014

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Transcript of Transformations

Vector and Prime Notation
Line Segment
Parallel Lines
Parallel lines
never intersect!
Parallel lines can go on forever, or they can stop.
Perpendicular lines always have to have a
right angle
.
Perpendicular lines also
always intersect.
Lines
Composition of Transformations
A composition of transformations is the
result
of performing/ putting more than one composition.
The symbol is an open circle.
You must do it in order, and you read it left to right.
Glide Reflections
A glide rotation is a
translation
and a
reflection
that is preformed one after another.
Glide reflections are
commutative
because the line of reflection is parallel to the direction of the transformation.
Reflections
Re
fl
ections - Flip
Reflections are also isometries.
The rules for reflections are-

Reflect over x-axis- (x,y) (x,-y)
Reflect over y-axis- (x,y) (-x,y)
Reflect over y=x- (x,y) (y,x)
Reflect over y=-x- (x,y) (-y,-x)
Reflect over origin- (x,y) (-x.-y)



Rotations
MATH
With Fredrick the Fish

Translation
Tran
sl
ation- Slide
Translations are isometries.
Translations can be written in three ways, Ex.
To the left 2 units and up 4 units.
Prime Notation- (x,y) (x-2,y+4)
Vector Notation- (x,y) <-2,4>
Rota
t
ions- turn
Rotations are also isometies.
The rules for rotations-
90 degrees - (x,y) (-y,x)
180 degrees- (x,y) (-x,-y)
270 degrees- (x,y) (y,-x)
Dilations
Dilation- Little/Large
Dilations are NOT isometries!!!
Dilations have
scale factors
- Scale Factors are the ratios to make the
pre-image
larger or smaller.

The dialation formula is (x,y) (kx,ky). K is the scale factor.

Perpendicular Lines
A line segment has
2 end points
.
A line segment also
does not go on forever.
Vector notation is written like-

(x,y) <x,y>

Prime Notation is written like-

(x-2, y+4)
Vector and prime notation are ways to write a translation.
Definitions
Angles
There are three kinds of angles-

Obtuse angle
- An angle that is greater then 90 degrees.

Right angle
- An angle that is 90 degrees.

Acute angle
- An angle that is less than 90 degrees.
Plane
A
flat
surface.
Origin
The origin is the (0,0) mark on the graph.
Rotational Symmetry
Rotational Symmetry is when you can rotate a shape and it still looks the same.
Equiangular and Equilateral

Equiangular
is when more than two angles are the same.
Equilateral
is when more than two sides are the same.
Order
Order is numbers arranged sequentially.

example-
1,2,3,4,5,6,7,8,9,10


Bisector
A bisector is a line that passes through a shape evenly.
Congruent
When shapes are exactly the same.
Orientation
Orientation is the way something is positioned.
Full transcript