GEOMETRIC
TRANSFORMATION
CATEGORIES OF TRANSFORMATIONS
01
Rigid
Transformation
Are transformations
that do not change the
shape or size of the
preimage.
02
Non-Rigid
Transformation
Are transformations
that change the size
but not the shape of
the preimage.
DIFFERENT TYPES
01
Translation
Moving an object in space
without changing its size,
shape or orientation.
03
Glide Reflection
02
Reflection
Flipping an object across a line
without changing its size or
shape.
04
Rotation
05
Dilation
Translation of an object along Rotating an object about a Expanding or contracting an
a line then reflecting the fixed point without changing object without changing its
its size or shape.
shape or orientation.
translated object along a line
without changing its size or
shape.
01
TRANSLATION
In the game, pac-man’s goal is
to eat all the peas without
getting killed by the ghosts. In
this example we can see pacman in the box. This is the preimage. When the game starts,
pac-man begins moving and
translates his position into the
new image.
REFLECTION
The picture shown on the
right is a good example
of a reflection
transformation. The preimage buildings are
being reflected by the
water and creates this
picturesque scene.
Mars
Despite being red,
Mars is actually a cold
place
Neptune
GLIDE REFLECTIONS
The footprints on the sand
can be an example of glide
reflections because as
shows, pre-image footprint
1 is translated along the
red line, then reflected on
it forming footprint 2 as
the image.
2
1
ROTATIONS
In the photo, the part of
the wheel with the
number 1 on it symbolizes
the pre-image. Assuming
that the center of the
wheel is the fixed point of
the rotation, the pink
shaded part of the wheel
is the image when the
pre-image is rotated.
1
05
Did you know when we are in
conditions of low light, our eyes
automatically dilate in order to
allow more light to reach the
retina? In the picture below, the
pupil of the eye is a good
example of dilation where the
object changes its size but not
its position or shape.
PRACTICAL EXERCISE
The idea was to use one shape to form
the pieces of the clock. I used the
rotations, reflections, translations and
dilations to create the clock.
At first I made the circle outline. Then, I
made the pre-image oval to represent the
12th hour. I then dilated it to represent the
in-betweens of every digit. I then rotated
the dilated image by 15º. Then I rotated
both the hour and the dilated image
through half the clock. Then I reflected it
to make the other half of the clock. I then
created the hour hand and dilated it and
translated the image to form the minute
hand. The center in between the two
hands was then crated so that the
distinction can be seen.
THANKS
Resources:
● https://ilovemanchester.com/pac-man-inspiredmaze-manchester
● https://sunnemath.files.wordpress.com/2012/10/
reflectionsym22.png
● https://www.pbslearningmedia.org/resource/mu
en-math-g-rotation/rotation/
● https://www.scienceabc.com/wpcontent/uploads/2017/02/Pupil-dilation.jpg
● https://www.walmart.com/ip/Great-BIG-CanvasFootprints-In-The-Sand-Poster-Print/145840829
● https://slidesgo.com/