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Transformation
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Concept

Transformation

A transformation is a function that changes a figure in a particular way — it can change the position, size, and orientation of a figure. The original figure is called the preimage and the produced figure is called the image of the transformation. To denote the image of a labeled point, a prime symbol is added next to the previous label.
A triangle and its image under a transformation
Transformations are sometimes expressed as a mapping. That is, it maps the inputs to the outputs. Note that the input can be a single point.
Here, T is the transformation, (x,y) are the coordinates of the points of the preimage, and are the coordinates of the points of the image.
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