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Transformations

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Angus Warren

on 10 May 2014

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Transcript of Transformations

Angus Warren
Transformations
There are four basic types of transformation.
What is a Transformation?
any change made to a geometric figure's location, orientaion, shape, or size.
A Transformation is
and other vocab.
An Isometry is
any transformation in which the preimage and image are congruent.
A Preimage is
the original figure
An Image is
the figure after transformation
These are reflection, rotation, translation, and glide reflection.
All of the transformations occur often in the real world.
Watch and ye shall see.
Reflection
is the flipping of an object or series of objects across a given line.
almost...
Here's the line of reflection.
Rotation
is the turning of an object a certain number of degrees around a given point.
Translation
is the movement of an object across a plane following a given rule of translation.
Glide Reflection
is the combination of the translation of an object and the reflection of the same object across a line parallel to the line of translation.
270 degrees
90 degrees
point of rotation
40 degrees
180 degrees
270 or 90 degrees
This translation occurs straight down the imagined y-axis
In this double transformation, pillar A translates to B, B goes to C, and C translates to D along the imagined x-axis.
A
B
C
D
Translations are riddled throughout this one.
1.
2.
3.
1.
2.
3.
Translation
Reflection
or
Reflection
Translation
Though this next one is technically not a glide reflection because the line of reflection is not parallel to the line of translation, it comes close.
Reflection
Translation
Translation
Reflection
The Classic
The motion of a knight in chess.
All of them appear frequently in the real world.
Using these 4 basic transformations, a whole series of composite transformations can be made.
FIN
A prime example is the knight's actual motion.
Translation
Reflection
Many other normal and composite transformations can be found, often in architecture, games, art, and everyday objects such as automobiles.
This one may be incorrect, because I do not know exactly how many blades there are here.
Full transcript