Transformation IGCSE

Quiz 1:
 Fullscreen Mode

Geometric Transformations Theory

1. Reflections

Definition: Mirror image over a line

Key Formulas:

- Vertical line x=a: (x,y) → (2a-x,y)
- Horizontal line y=b: (x,y) → (x,2b-y)
- Line y=x: (x,y) → (y,x)
- Line y=-x: (x,y) → (-y,-x)

2. Rotations

Definition: Turning around a center point

Rotation Matrices:

90° clockwise:
\(\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\)

180° rotation:
\(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\)

3. Translations

Definition: Sliding without rotation

Vector Notation:

Translation vector \( \binom{a}{b} \):
(x,y) → (x+a, y+b)

4. Enlargements

Scale Factor Formula:

For center (h,k) and scale factor s:
x' = h + s(x - h)
y' = k + s(y - k)

Combined Transformations

Multiple transformations can be represented as:

Composite Transformation Matrix:
T = T₁ × T₂ × ... × Tₙ

Key Concepts:

• Congruence in reflection/rotation/translation
• Similarity in enlargements
• Invariant points/lines
• Matrix representation of transformations