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Supporting Australian Mathematics Project: Middle years.

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Year 7

Measurement and Geometry

Transformations of the plane

Cartesian plane shown with right-angled triangles T, T', T'' and T'''.
Detailed description

Each of the triangles \(T^\prime\), \(T^{\prime\prime}\) and \(T^{\prime\prime\prime}\) are obtained from triangle \(T\) by moving it.

Triangle \(T^\prime\) is formed by rotating triangle \(T\) about the point \(C\).

Triangle \(T^{\prime\prime}\) is formed by reflecting triangle \(T\) in the \(y\)-axis.

Triangle \(T^{\prime\prime\prime}\) is formed by translating triangle \(T\) across and down.

When the triangle is moved in this way we call the movement a transformation. The three types of transformations considered in this resource package are translations, reflections and rotations.

Properties of these transformations

When a figure is translated, rotated or reflected:

  • Line segments move to intervals of the same length
  • Angles move to angles of the same size.