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.