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.