Transformations

Spec reference: Geometry and measures - Transformations
Key idea: Perform and describe translations, reflections, rotations and enlargements.

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Translation

A translation moves a shape without rotating or reflecting it.

Described by a column vector $(\genfrac{}{}{0ex}{}{x}{y})$: $x$ = right (negative = left), $y$ = up (negative = down).

Example

Translate by $(\genfrac{}{}{0ex}{}{3}{-2})$ means 3 right, 2 down.

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Reflection

A reflection flips a shape in a mirror line.

Common mirror lines: $x=a$, $y=b$, $y=x$, $y=-x$

Example

Reflecting in $y=x$: swap the $x$ and $y$ coordinates. $(3,1)\to (1,3)$

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Rotation

A rotation turns a shape about a centre of rotation by a given angle and direction (clockwise or anticlockwise).

Always state: angle, direction, centre.

Example

A $90°$ clockwise rotation about the origin: $(x,y)\to (y,-x)$

A $180°$ rotation about the origin: $(x,y)\to (-x,-y)$

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Enlargement

An enlargement changes the size of a shape using a scale factor $k$ and a centre of enlargement.

• $k>1$: shape gets bigger
• $0<k<1$: shape gets smaller
• $k<0$: shape flips and changes size

$$\text{Image length}=k\times \text{object length}$$

Example

Enlarge by scale factor 3 from centre $(0,0)$: multiply all coordinates by 3.

$(2,1)\to (6,3)$

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Describing transformations

When describing a transformation, you must give all required information:

Type	Required information
Translation	Column vector
Reflection	Mirror line equation
Rotation	Angle, direction, centre
Enlargement	Scale factor, centre of enlargement

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Congruence and similarity

• Congruent shapes: same shape AND size (translations, reflections, rotations)
• Similar shapes: same shape but different size (enlargements)

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Exam tips

Watch out for

• Always give ALL required details when describing a transformation
• For rotation, check the direction (clockwise vs anticlockwise)
• A negative scale factor means the image is on the other side of the centre

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Test Yourself

Question 1 of 5

Describing a rotation needs: