Transformation: Shapes in Motion

Transformation

Transformation is a function that moves or changes a figure in some way to produce a new figure call an image. Another name for the
the original figure is the pre-image.

There are five types of transformations they are following:

1. 1. Reflections

   2. Translations

   3. Rotations

   4. Dilations

1. Reflection

Line reflections are isometries that do not preserve orientation. Therefore line reflections are opposite isometries. Thus, a reflected image in a mirror appears “backwards.”Every points are the same distance from the central line

2. Translation

A translation “slides” an object a fixed distance in a given direction. The original and its translation have the same shape and size, and they face in the same direction, A translation creates a figure that is congruent with the original fig and preserves distance and orientation. A translation is a direct isometry.

A translation (notation T_a,b) is a transformation of the plane that slides every point of a figure the same distance in the same direction.

3. Rotation

A rotation about a fixed point, called the center of rotation, through an angle of xⁿ maps a point to its image such that if the point is the center of rotation, then the image and preimage are the same points, or if the point is not the center of rotation, then the image and [reimage are the same distance from the center of rotation and the measure of the angle of rotation formed by the preimage, center of rotation, and image points are x.

4. Dilations

The dilation is a transformation in which a figure is enlarged or reduced with respect to a fixed point C called the Center of Dilation. Dilation is not a rigid motion. It does not preserve distance and is not an isometry.

Also read, Reasoning and Parallel line