Geometric Transformations
by D. Fisher
Learning Targets
I can draw transformations of reflections,
rotations, translations and
combinations of these using graph
paper, transparencies, and /or geometry
software.
Key Questions
• What is a transformation?
• What is a pre-image?
• What is an image?
• Image –
is the new figure. Image after the
transformations.
• Preimage –
the original figure. Image before the
transformations.
Transformation
• Transformation – In a plane, a mapping for
which each point has exactly one image
point and each image point has exactly one
preimage point.
• Reflection - A transformation representing a
flip of a figure over a point, line, or plane.
Rotation
• Rotation - A transformation that turns every
point of a preimage through a specified
angle and direction about a fixed point,
called the center of rotation. Rotate.
• Translation – A transformation that moves
all points of a figure the same distance in
the same direction. A slide.
1.
Reflection, Rotation, or Translation
Rotation
2.
Reflection, Rotation, or Translation
Reflection
3.
Reflection, Rotation, or Translation
Translation
4.
Reflection, Rotation, or Translation
Reflection
5.
Reflection, Rotation, or Translation
Rotation
6.
Reflection, Rotation, or Translation
Translation
7.
Reflection, Rotation, or Translation
Reflection
8.
Reflection, Rotation, or Translation
Translation
9.
Reflection, Rotation, or Translation
Rotation
10.
Why is this not perfect reflection?
This is not a perfect reflection because the zebras have slightly
different striping. One has its nose closer to the ground.
11.
Reflection, Rotation, or Translation
Translation
12.
Reflection, Rotation, or Translation
Reflection and rotation of
o
180 .
13.
Reflection, Rotation, or Translation
Rotation
14.
Reflection, Rotation, or Translation
Reflection in several directions.
15.
Reflection, Rotation, or Translation
Rotation
16.
Reflection, Rotation, or Translation
Reflection. Note the position of the purple tips;
rotation of 180o would cause the top purple tip to
be on the bottom.
17.
Reflection, Rotation, or Translation
Translation
18.Reflection, Rotation, or Translation
Reflection in multiple mirrors
19.
Reflection, Rotation, or Translation
Translation. Watch the colors.
20.
Reflection, Rotation, or Translation
Reflection. Note the position of the red parts.
21.
Reflection, Rotation, or Translation
Rotation.
Note the red parts.
22.
The End
The top left and the bottom right are reflections; the
top right and the two on the bottom are rotations.