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.
A compositions of transformations
means that two or more transformations will be performed on one object. For instance, we could perform
and then a translation
on the same point.
Important terms & defintions
: The figure after the transformation.
: the figure prior to the transformation.
- 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.
- On the other hand,a dilation is not an isometry becuase its image is not congruent with its pre-image.