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.