Transformation Geometry
Reflections, rotations, translations and enlargements
Transformation Geometry
Transformations change the position or size of a shape on the Cartesian plane:
• Translation: slide (x + a, y + b)
• Reflection: mirror image over a line
• Rotation: turn around a point
• Enlargement: change size by a scale factor
Example
Rules for Common Transformations
Reflection in x-axis: (x, y) → (x, −y)
Reflection in y-axis: (x, y) → (−x, y)
Reflection in y = x: (x, y) → (y, x)
Rotation 90° clockwise about origin: (x, y) → (y, −x)
Rotation 180° about origin: (x, y) → (−x, −y)
Example
Enlargement
Enlarge point (2, 3) by scale factor 3 from origin:
(2×3, 3×3) = (6, 9)
Enlarge triangle with vertices (1,1), (3,1), (2,4) by factor 2:
→ (2,2), (6,2), (4,8)
Note
Remember
Translation, reflection and rotation preserve shape and size (isometric). Enlargement changes size but preserves shape. Describe every transformation fully: type, direction/line/centre and amount.
Key Vocabulary
TranslationSliding a shape without rotating or reflecting
ReflectionA mirror image of a shape over a line
RotationTurning a shape around a centre point
EnlargementScaling a shape by a factor from a centre point
IsometricA transformation that preserves shape and size
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