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by D. Fisher
Geometric Transformations
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.
Reflection, Rotation, or Translation1.
Rotation
Reflection, Rotation, or Translation2.
Reflection
Reflection, Rotation, or Translation3.
Translation
Reflection, Rotation, or Translation4.
Reflection
Reflection, Rotation, or Translation5.
Rotation
Reflection, Rotation, or Translation6.
Translation
Reflection, Rotation, or Translation7.
Reflection
Reflection, Rotation, or Translation8.
Translation
Reflection, Rotation, or Translation9.
Rotation
Why is this not perfect reflection?10.
This is not a perfect reflection because the zebras have slightly different striping. One has its nose closer to the ground.
Reflection, Rotation, or Translation11.
Translation
Reflection, Rotation, or Translation12.
Reflection and rotation of 180o.
Reflection, Rotation, or Translation13.
Rotation
Reflection, Rotation, or Translation14.
Reflection in several directions.
Reflection, Rotation, or Translation15.
Rotation
Reflection, Rotation, or Translation16.
Reflection. Note the position of the purple tips; rotation of 180o would cause the top purple tip to be on the bottom.
Reflection, Rotation, or Translation17.
Translation
Reflection, Rotation, or Translation18.
Reflection in multiple mirrors
Reflection, Rotation, or Translation19.
Translation. Watch the colors.
Reflection, Rotation, or Translation20.
Reflection. Note the position of the red parts.
Reflection, Rotation, or Translation21.
Rotation. Note the red parts.
The End
The top left and the bottom right are reflections; the top right and the two on the bottom are rotations.
22.