Transformations in math

Translations, reflections, rotations

A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation.

Translation
Reflection
- point reflection
Rotation
Dilation

A compositions of transformations means that two or more transformations will be performed on one object. For instance, we could perform a reflection and then a translation on the same point.

interesting theorems

composition of reflections

Important terms & defintions

Preimage
: the figure prior to the transformation.

Image

Isometry
: a transformation that preserves congruence. In other words, a transformation in which the image and preimage have the same side lengths and angle measurements. The following transformations maintain their mathematical congruence.
- Translations (a translation is considered a 'direct isometry' because it not only maintains congruence, but it also, unlike reflections and rotations, preserves its orientation.
- Rotations
- Reflections
- Dilations
On the other hand,a dilation is not an isometry becuase its image is not congruent with its pre-image.

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Transformations in math

Translations, reflections, rotations

Important terms & defintions

Preimage

Image

Isometry