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24.8 Summary

  • An ordered pair consists of an \(x\)-value called the \(x\)-coordinate and a \(y\)-value called the \(y\)-coordinate. Notation: \((x; y)\)
  • Translating a shape means sliding a shape from one position to another.
  • Reflecting a shape means flipping a shape over a line of reflection or a mirror line.
  • Reflecting \(P(x; y)\) in the \(x\)-axis produces image \(P'(x; -y)\): \[(x; y) \rightarrow (x; -y)\]
  • Reflecting \(P(x; y)\) in the \(y\)-axis produces image \(P'(-x; y)\): \[(x; y) \rightarrow (-x; y)\]
  • Rotating a shape means turning a shape around the centre of rotation.
  • A rotation transformation has three components:

    • the angle of rotation
    • the centre of rotation
    • the direction of rotation.
  • A clockwise direction means turning in the same direction as the hands of a clock.
  • An anti-clockwise direction means turning in the opposite direction to the direction of the hands of a clock.
  • Enlarging a shape means making a shape bigger by a scale factor.
  • Reducing a shape means making a shape smaller by a scale factor.
  • An enlargement or reduction transformation has two components:

    • the scale factor
    • the centre of enlargement/reduction
  • For enlargement transformations, the scale factor is \(> 1\).
  • For reduction transformations, the scale factor is a fraction between 0 and 1.
  • Perimeter of the image = scale factor \(\times\) perimeter of the shape.
  • Area of the image = (scale factor)\(^2 \times\) area of the shape.