Transformations

A transformation of a geometric figure is a change in its position, shape, or size. The original figure is called the preimage, and the transformed figure is called the image. A transformation in which the preimage and image are congruent is called an isometry.

I. Translations

A translation is an isometry that maps all points of a figure the same distance in the same direction.

1. Change the magnitude and direction of vector u and observe the resulting image. Explain how a vector may be used to represent a translation.
2. Use a vector to translate the preimage 3 units left and 2 units down.
3. Use a vector to show the translation: .
4. Identify the vector used in the transformation shown below. Describe your method.

II. Reflections

A reflection is an isometry in which a figure and its image have opposite orientations.

1. Change the line of reflection and observe the resulting image.
2. Change the line of reflection so that one of the points in the preimage is on the line. Describe the corresponding point in the image.
3. Make the axes visible and reflect the preimage across the line x=6.
4. Make the axes visible and reflect the preimage across the line y=1-0.25x.
5. Identify the line of symmetry for the transformation shown below. Describe your method.

III. Rotations

When describing a rotation, you must identify the center of rotation, the angle of rotation, and the direction (clockwise or counter-clockwise).

1. Use the slider to change the angle of rotation and observe the resulting image.
2. Move the center of rotation and observe the resulting image.
3. Move the center of rotation so that it is the same as one of the points in the preimage. Describe the corresponding point in the image.
4. Find the center of rotation for the transformation shown below. Describe your method.