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There are four main types of transformations: translation, rotation, reflection and dilation.
There are three basic rigid transformations: reflections, rotations, and translations. Reflections reflect the shape across a line which is given. Rotations rotate a shape around a center point which is given. Translations slide or move a shape from one place to another.
Transformation involves moving an object from its original position to a new position. The object in the new position is called the image. Each point in the object is mapped to another point in the image. The following figures show the four types of transformations: Translation, Reflection, Rotation, and Dilation.
Vertical Shifts. Horizontal Shifts. Reflection about the x-axis. Reflection about the y-axis. Vertical shifting or stretching. Horizontal shifting or stretching.
When two or more transformations are combined to form a new transformation, the result is called a sequence of transformations, or a composition of transformations. Remember, that in a composition, one transformation produces an image upon which the other transformation is then performed.
Reflections, translations, rotations, and combinations of these three transformations are “rigid transformations”. A reflection is called a rigid transformation or isometry because the image is the same size and shape as the preimage.
When combining horizontal transformations written in the form f(bx+h) f (b x + h) , first horizontally shift by h and then horizontally stretch by 1b. Horizontal and vertical transformations are independent. It does not matter whether horizontal or vertical transformations are performed first.
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