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3.1 Transformation 1: Translation


  • The Cartesian plane is represented by the set R^2 of all ordered pairs of real numbers. That is, R^{2}=\{(x, y): x, y \in R\}.
  • If there is a rule that maps all points (let’s say one of it is denoted as \left(x_{1},\ y_{1}\right)) to their respective new points (denoted as \left(x_{2},\ y_{2}\right)), this rule is said as a transformation.
  • A transformation is generally represented by the following:

(x,\ y) \rightarrow\left(x^{\prime},\ y^{\prime}\right)

  • There will be three transformations introduced in this course, namely translation, reflection and dilation. Combinations of these is also introduced.


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