Transformations
Transformations are all about moving shapes on a grid. From sliding and flipping to turning and resizing, understanding these four key movements is essential for geometry, design, and your GCSE Maths exam.
The Four Key Transformations
Translation (A Slide)
The shape slides from one position to another without changing its size or orientation. Describe it with a column vector.
Reflection (A Flip)
The shape is flipped over a mirror line. Describe it with the equation of the mirror line (e.g., $x=2$ or $y=x$).
Rotation (A Turn)
The shape turns around a fixed point. Describe it with three things: the angle, direction (clockwise or anticlockwise), and centre of rotation.
Enlargement (A Resize)
The shape is made bigger or smaller but stays in proportion. Describe it with a scale factor and a centre of enlargement.
Worked Examples
Example 1: Translation
Translate triangle A by the vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$.
Move every point 3 right and 2 up.
Example 2: Reflection
Reflect shape C in the line $y=0$ (the x-axis).
Each point moves the same distance from the mirror line but to the opposite side.
Tutor Insights
🤔 Common Misunderstandings
- Mixing up coordinates in translation vectors — the top number is horizontal, the bottom is vertical.
- Forgetting all three parts of a rotation description: angle, direction, and centre.
- Assuming the centre must be the origin. The centre of enlargement or rotation can be any point!
📝 Common Exam Mistakes
- Incomplete descriptions. Just writing “rotation” scores zero — you must give full details.
- Inaccurate drawing. Always use a ruler and count squares carefully.
- Rotation confusion. Use tracing paper for rotations — always ask for it in an exam!
Practice Questions
- Describe fully the transformation that maps shape A onto shape B.
- Draw the image of triangle P after a reflection in the line $x=2$.
- Draw the image of shape R after a rotation of $180°$ about the point $(1,1)$.
Show Answers
- Answer: Translation by the vector $\begin{pmatrix} 3 \\ 3 \end{pmatrix}$.
- Answer: The new vertices will be at $(4,4)$, $(4,6)$, $(3,6)$, and $(3,4)$.
- Answer: The new vertices will be at $(-2,0)$, $(-4,0)$, $(-4,-1)$, and $(-2,-1)$.
Need Help with Transformations?
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