Home » VCE » Maths Methods U3 & 4 Master Notes » Transformation 1: Translation

# Transformation 1: Translation

## 3.4 Combination of Transformations

#### Illustrating Combination of Transformations

• Transformations that we learnt previously (reflection, translation, dilation) can be combined together.
• It is combined simply applying the transformation in an ordered manner.
• For example, first consider:
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## 3.1 Transformation 1: Translation

#### Transformation

• 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.

#### Translation

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## Matrices and Linear Transformations

This tutorial covers material encountered in chapters 2 and 3 of the VCE Mathematical Methods Textbook, namely: Simultaneous equations Matrices and their components Algebra of… Read More »Matrices and Linear Transformations