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Learning goals

**Learning Goals**

- Understand the four transformations: translations, rotations, reflections, enlargements

Maths

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There are four main ways to mathematically alter a shape: translation, rotation, reflection and enlargement.

Translating a shape means to move its position while keeping the orientation and size of the shape intact. Translations are described using column vectors $\begin{pmatrix}x\\y\end{pmatrix}$, which means to move the shape $x$ spaces to the right and $y$ spaces up.

*The square $ABCD$ was originally in the top-right quadrant. It was then transformed to the bottom-left quadrant as shown below. Describe the transformation that took place.*

*The size and orientation of the shape is unchanged, so the shape has been translated. *

*To find the corresponding column vector, focus on one vertex and see where it moved to.*

$A=(1,1)$ *gets mapped to $A=(-4,-4)$.*

*The corresponding column vector is therefore $\begin{pmatrix}-5\\-5\end{pmatrix}$ as $A$ moved $5$ steps to the left and $5$ steps down to end up at $(-4,-4)$.*

*The transformation is a **translation** by column vector *$\underline{\begin{pmatrix}-5\\-5\end{pmatrix}}$__.__

Rotating a shape has three details associated with it:

- The angle by which the shape has been rotated.
- The direction of rotation (clockwise or anticlockwise).
- The centre of rotation.

The *centre of rotation* is the point you rotate everything around.

*Describe the transformation that maps the shape $ABCD$ to the shape $A'B'C'D'$ in the diagram below.*

*This is a **rotation** of *$\underline{180 \degree}$* with centre **O**.*

**Note: **In this case, there was no need to specify direction as a rotation of $180^\circ$ clockwise is the same as a rotation of $180^\circ$