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# Test yourself now

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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.