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    Transformations in math

    Translations, reflections, rotations

    Transformations Home | Translation in Math | Reflection in Math |Rotation in Math |compositions of transformations | composition of reflections | Theorems involving reflections | images
    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 a reflection and then a translation on the same point.

    Important terms & defintions

    • Preimage

      : the figure prior to the transformation.

    • Image

      : The figure after 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.
      • 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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