Home » VCE » Maths Methods U3 & 4 Master Notes » Transformation 3: Reflections

# Transformation 3: Reflections

## 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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## 3.3 Transformation 3: Reflection

#### Reflection

• Reflection is a more familiar transformation to us: we usually see our reflections in a mirror.
• In Cartesian plane, a line will be the ‘mirror’, and the function will be reflected along the ‘mirror’. Therefore, the line can be horizontal, vertical, or diagonal. Here, we will only consider horizontal and vertical reflection, as diagonal reflections are too complex for this course. In particular, we will only study reflections along the x-axis and y-axis.
• A reflection along the x-axis gives the following transformation:

(x,\ y) \rightarrow(x,\ -y)

y=-f(x)

and a reflection along the y-axis gives the following transformation:

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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