Transformations
Year 8 📐 Geometry & Measures Reflection, rotation, translation and enlargement.
🔄 The Four Transformations
The four transformations are translation, reflection, rotation, and enlargement. The first three preserve size and shape.
| Transformation | What changes? | What stays the same? |
|---|---|---|
| Translation | Position | Shape, size, orientation |
| Reflection | Position, orientation | Shape, size |
| Rotation | Position, orientation | Shape, size |
| Enlargement | Size, position | Angles, shape |
↔️ Describing Transformations Fully
Each transformation requires specific information to describe it completely.
- Translation: give the column vector $\begin{pmatrix}x\y\end{pmatrix}$
- Reflection: give the mirror line equation (e.g. $y = x$, $x = 2$)
- Rotation: give the centre, angle, and direction (CW or ACW)
- Enlargement: give the centre and scale factor $k$
Always name the transformation first before giving the required details.
🔍 Enlargement and Scale Factor
An enlargement with scale factor $k$ multiplies every length by $|k|$, but angles are unchanged.
⚡ Scale Factor
$$k = \frac{\text{image length}}{\text{original length}}$$Example: If $k = -2$, the image is twice as large and on the opposite side of the centre of enlargement.
A fractional scale factor (e.g. $k = 0.5$) makes the image smaller than the original.
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Interactive Demonstration — Transformations
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🔄 Transformation Explorer
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